{"id":220982,"date":"2026-01-29T11:57:11","date_gmt":"2026-01-29T09:57:11","guid":{"rendered":"https:\/\/azbuki.bg\/?p=220982"},"modified":"2026-01-29T11:57:11","modified_gmt":"2026-01-29T09:57:11","slug":"geometrichni-mesta-porodeni-ot-ravnostranni-triagalniczi-s-varhove-varhu-okrazhnost","status":"publish","type":"post","link":"https:\/\/strategies.azbuki.bg\/en\/uncategorized\/geometrichni-mesta-porodeni-ot-ravnostranni-triagalniczi-s-varhove-varhu-okrazhnost\/","title":{"rendered":"Loci, Generated by Equilateral Triangles with Vertices Lying on a Circle"},"content":{"rendered":"<p><strong>Borislav Borisov,<\/strong><br \/>\n<strong>Deyan Dimitrov,<\/strong><br \/>\n<strong>Nikolay Ninov,<\/strong><br \/>\n<strong>Teodor Hristov<\/strong><\/p>\n<p><em>Mathematics High School \u2013 Lovech<\/em><\/p>\n<p><strong>Abstract.<\/strong> The article is a scientific work of student under the supervision of Associate Professor Dr. Veselin Nenkov. The new results in it were awarded first prize at the International Competition \u201cMethodology and Information Technology in Education\u201d in 2019. The article refers to loci determined by notable points in a triangle, generated by equilateral triangles with vertices on a constant circle. The construction of the triangle is similar to the initial one from the First International \u201cNetwork research project\u201d with the participation of Bulgaria, Kazakhstan, and Russia. The main difference between those two constructions consists in the location of two pairs of vertices of the two equilateral triangles \u2013 in the initial problem they are on a constant line, but in the present one \u2013 on a circle. The loci are circles, ellipses, and curves of fourth order.<\/p>\n<p><em>Keywords:<\/em> equilateral triangle; circle; ellipse; curve of fourth degree<\/p>\n<p><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2026\/01\/math_info_2_19_borisov_co.pdf\">>> Download the article as a PDF file <<<\/a><\/p>","protected":false},"excerpt":{"rendered":"<p>\u0411\u043e\u0440\u0438\u0441\u043b\u0430\u0432 \u0411\u043e\u0440\u0438\u0441\u043e\u0432, \u0414\u0435\u044f\u043d \u0414\u0438\u043c\u0438\u0442\u0440\u043e\u0432, \u041d\u0438\u043a\u043e\u043b\u0430\u0439 \u041d\u0438\u043d\u043e\u0432, \u0422\u0435\u043e\u0434\u043e\u0440 \u0425\u0440\u0438\u0441\u0442\u043e\u0432 \u041f\u0440\u0438\u0440\u043e\u0434\u043e-\u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0430 \u0433\u0438\u043c\u043d\u0430\u0437\u0438\u044f \u2013 \u041b\u043e\u0432\u0435\u0447 \u0420\u0435\u0437\u044e\u043c\u0435. \u0421\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0435 \u0443\u0447\u0435\u043d\u0438\u0447\u0435\u0441\u043a\u0430 \u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u043a\u0430 \u043f\u043e\u0434 \u0440\u044a\u043a\u043e\u0432\u043e\u0434\u0441\u0442\u0432\u043e\u0442\u043e \u043d\u0430 \u0434\u043e\u0446. \u0434-\u0440 \u0412\u0435\u0441\u0435\u043b\u0438\u043d \u041d\u0435\u043d\u043a\u043e\u0432. \u041d\u043e\u0432\u0438\u0442\u0435 \u0440\u0435\u0437\u0443\u043b\u0442\u0430\u0442\u0438 \u0432 \u043d\u0435\u044f \u043f\u043e\u043b\u0443\u0447\u0438\u0445\u0430 \u043e\u0442\u043b\u0438\u0447\u043d\u0430 \u043e\u0446\u0435\u043d\u043a\u0430 \u043f\u043e \u0432\u0440\u0435\u043c\u0435 \u043d\u0430 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u044f\u043d\u0435\u0442\u043e \u0454 \u0432 \u043c\u0435\u0436\u0434\u0443\u043d\u0430\u0440\u043e\u0434\u043d\u0438\u044f \u043a\u043e\u043d\u043a\u0443\u0440\u0441 \u201e\u041c\u0435\u0442\u043e\u0434\u043e\u043b\u043e\u0433\u0438\u044f \u0438 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u043e\u043d\u043d\u0438 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0438 \u0432 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0435\u0442\u043e\u201c \u043f\u0440\u0435\u0437 2019 \u0433. \u0438 \u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u043a\u0430\u0442\u0430 \u0431\u0435\u0448\u0435 \u0443\u0434\u043e\u0441\u0442\u043e\u0435\u043d\u0430 \u0441 \u043f\u044a\u0440\u0432\u0430 \u043d\u0430\u0433\u0440\u0430\u0434\u0430. [&hellip;]<\/p>","protected":false},"author":124332423427287,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jnews-multi-image_gallery":[],"jnews_single_post":[],"jnews_primary_category":[]},"categories":[1],"tags":[16163,16164,15096,16162],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u0413\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0438 \u043c\u0435\u0441\u0442\u0430, \u043f\u043e\u0440\u043e\u0434\u0435\u043d\u0438 \u043e\u0442 \u0440\u0430\u0432\u043d\u043e\u0441\u0442\u0440\u0430\u043d\u043d\u0438 \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u0446\u0438 \u0441 \u0432\u044a\u0440\u0445\u043e\u0432\u0435 \u0432\u044a\u0440\u0445\u0443 \u043e\u043a\u0440\u044a\u0436\u043d\u043e\u0441\u0442 - \u0410\u0437-\u0431\u0443\u043a\u0438<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/pedagogy.azbuki.bg\/en\/uncategorized\/geometrichni-mesta-porodeni-ot-ravnostranni-triagalniczi-s-varhove-varhu-okrazhnost\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u0413\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0438 \u043c\u0435\u0441\u0442\u0430, \u043f\u043e\u0440\u043e\u0434\u0435\u043d\u0438 \u043e\u0442 \u0440\u0430\u0432\u043d\u043e\u0441\u0442\u0440\u0430\u043d\u043d\u0438 \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u0446\u0438 \u0441 \u0432\u044a\u0440\u0445\u043e\u0432\u0435 \u0432\u044a\u0440\u0445\u0443 \u043e\u043a\u0440\u044a\u0436\u043d\u043e\u0441\u0442 - \u0410\u0437-\u0431\u0443\u043a\u0438\" \/>\n<meta property=\"og:description\" content=\"\u0411\u043e\u0440\u0438\u0441\u043b\u0430\u0432 \u0411\u043e\u0440\u0438\u0441\u043e\u0432, \u0414\u0435\u044f\u043d \u0414\u0438\u043c\u0438\u0442\u0440\u043e\u0432, \u041d\u0438\u043a\u043e\u043b\u0430\u0439 \u041d\u0438\u043d\u043e\u0432, \u0422\u0435\u043e\u0434\u043e\u0440 \u0425\u0440\u0438\u0441\u0442\u043e\u0432 \u041f\u0440\u0438\u0440\u043e\u0434\u043e-\u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0430 \u0433\u0438\u043c\u043d\u0430\u0437\u0438\u044f \u2013 \u041b\u043e\u0432\u0435\u0447 \u0420\u0435\u0437\u044e\u043c\u0435. \u0421\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0435 \u0443\u0447\u0435\u043d\u0438\u0447\u0435\u0441\u043a\u0430 \u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u043a\u0430 \u043f\u043e\u0434 \u0440\u044a\u043a\u043e\u0432\u043e\u0434\u0441\u0442\u0432\u043e\u0442\u043e \u043d\u0430 \u0434\u043e\u0446. \u0434-\u0440 \u0412\u0435\u0441\u0435\u043b\u0438\u043d \u041d\u0435\u043d\u043a\u043e\u0432. \u041d\u043e\u0432\u0438\u0442\u0435 \u0440\u0435\u0437\u0443\u043b\u0442\u0430\u0442\u0438 \u0432 \u043d\u0435\u044f \u043f\u043e\u043b\u0443\u0447\u0438\u0445\u0430 \u043e\u0442\u043b\u0438\u0447\u043d\u0430 \u043e\u0446\u0435\u043d\u043a\u0430 \u043f\u043e \u0432\u0440\u0435\u043c\u0435 \u043d\u0430 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u044f\u043d\u0435\u0442\u043e \u0454 \u0432 \u043c\u0435\u0436\u0434\u0443\u043d\u0430\u0440\u043e\u0434\u043d\u0438\u044f \u043a\u043e\u043d\u043a\u0443\u0440\u0441 \u201e\u041c\u0435\u0442\u043e\u0434\u043e\u043b\u043e\u0433\u0438\u044f \u0438 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u043e\u043d\u043d\u0438 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0438 \u0432 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0435\u0442\u043e\u201c \u043f\u0440\u0435\u0437 2019 \u0433. \u0438 \u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u043a\u0430\u0442\u0430 \u0431\u0435\u0448\u0435 \u0443\u0434\u043e\u0441\u0442\u043e\u0435\u043d\u0430 \u0441 \u043f\u044a\u0440\u0432\u0430 \u043d\u0430\u0433\u0440\u0430\u0434\u0430. [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/pedagogy.azbuki.bg\/en\/uncategorized\/geometrichni-mesta-porodeni-ot-ravnostranni-triagalniczi-s-varhove-varhu-okrazhnost\/\" \/>\n<meta property=\"og:site_name\" content=\"\u0410\u0437-\u0431\u0443\u043a\u0438\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/Azbuki55\/\" \/>\n<meta property=\"article:published_time\" content=\"2026-01-29T09:57:11+00:00\" \/>\n<meta name=\"author\" content=\"\u201e\u0410\u0437-\u0431\u0443\u043a\u0438\u201c\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"\u201e\u0410\u0437-\u0431\u0443\u043a\u0438\u201c\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/pedagogy.azbuki.bg\/en\/uncategorized\/geometrichni-mesta-porodeni-ot-ravnostranni-triagalniczi-s-varhove-varhu-okrazhnost\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/pedagogy.azbuki.bg\/en\/uncategorized\/geometrichni-mesta-porodeni-ot-ravnostranni-triagalniczi-s-varhove-varhu-okrazhnost\/\"},\"author\":{\"name\":\"\u201e\u0410\u0437-\u0431\u0443\u043a\u0438\u201c\",\"@id\":\"https:\/\/vocedu.azbuki.bg\/en\/#\/schema\/person\/de220d282eaa494f914ce0fd838645dd\"},\"headline\":\"\u0413\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0438 \u043c\u0435\u0441\u0442\u0430, \u043f\u043e\u0440\u043e\u0434\u0435\u043d\u0438 \u043e\u0442 \u0440\u0430\u0432\u043d\u043e\u0441\u0442\u0440\u0430\u043d\u043d\u0438 \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u0446\u0438 \u0441 \u0432\u044a\u0440\u0445\u043e\u0432\u0435 \u0432\u044a\u0440\u0445\u0443 \u043e\u043a\u0440\u044a\u0436\u043d\u043e\u0441\u0442\",\"datePublished\":\"2026-01-29T09:57:11+00:00\",\"dateModified\":\"2026-01-29T09:57:11+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/pedagogy.azbuki.bg\/en\/uncategorized\/geometrichni-mesta-porodeni-ot-ravnostranni-triagalniczi-s-varhove-varhu-okrazhnost\/\"},\"wordCount\":164,\"publisher\":{\"@id\":\"https:\/\/vocedu.azbuki.bg\/en\/#organization\"},\"keywords\":[\"circle\",\"curve of fourth degree\",\"ellipse\",\"equilateral triangle\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/pedagogy.azbuki.bg\/en\/uncategorized\/geometrichni-mesta-porodeni-ot-ravnostranni-triagalniczi-s-varhove-varhu-okrazhnost\/\",\"url\":\"https:\/\/pedagogy.azbuki.bg\/en\/uncategorized\/geometrichni-mesta-porodeni-ot-ravnostranni-triagalniczi-s-varhove-varhu-okrazhnost\/\",\"name\":\"\u0413\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0438 \u043c\u0435\u0441\u0442\u0430, \u043f\u043e\u0440\u043e\u0434\u0435\u043d\u0438 \u043e\u0442 \u0440\u0430\u0432\u043d\u043e\u0441\u0442\u0440\u0430\u043d\u043d\u0438 \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u0446\u0438 \u0441 \u0432\u044a\u0440\u0445\u043e\u0432\u0435 \u0432\u044a\u0440\u0445\u0443 \u043e\u043a\u0440\u044a\u0436\u043d\u043e\u0441\u0442 - \u0410\u0437-\u0431\u0443\u043a\u0438\",\"isPartOf\":{\"@id\":\"https:\/\/vocedu.azbuki.bg\/en\/#website\"},\"datePublished\":\"2026-01-29T09:57:11+00:00\",\"dateModified\":\"2026-01-29T09:57:11+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/pedagogy.azbuki.bg\/en\/uncategorized\/geometrichni-mesta-porodeni-ot-ravnostranni-triagalniczi-s-varhove-varhu-okrazhnost\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/pedagogy.azbuki.bg\/en\/uncategorized\/geometrichni-mesta-porodeni-ot-ravnostranni-triagalniczi-s-varhove-varhu-okrazhnost\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/pedagogy.azbuki.bg\/en\/uncategorized\/geometrichni-mesta-porodeni-ot-ravnostranni-triagalniczi-s-varhove-varhu-okrazhnost\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/strategies.azbuki.bg\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"\u0413\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0438 \u043c\u0435\u0441\u0442\u0430, \u043f\u043e\u0440\u043e\u0434\u0435\u043d\u0438 \u043e\u0442 \u0440\u0430\u0432\u043d\u043e\u0441\u0442\u0440\u0430\u043d\u043d\u0438 \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u0446\u0438 \u0441 \u0432\u044a\u0440\u0445\u043e\u0432\u0435 \u0432\u044a\u0440\u0445\u0443 \u043e\u043a\u0440\u044a\u0436\u043d\u043e\u0441\u0442\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/vocedu.azbuki.bg\/en\/#website\",\"url\":\"https:\/\/vocedu.azbuki.bg\/en\/\",\"name\":\"\u0410\u0437-\u0431\u0443\u043a\u0438\",\"description\":\"\u041d\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u043d\u043e \u0438\u0437\u0434\u0430\u0442\u0435\u043b\u0441\u0442\u0432\u043e \u0437\u0430 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0435 \u0438 \u043d\u0430\u0443\u043a\u0430\",\"publisher\":{\"@id\":\"https:\/\/vocedu.azbuki.bg\/en\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/vocedu.azbuki.bg\/en\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/vocedu.azbuki.bg\/en\/#organization\",\"name\":\"\u0410\u0437-\u0431\u0443\u043a\u0438\",\"url\":\"https:\/\/vocedu.azbuki.bg\/en\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/vocedu.azbuki.bg\/en\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/azbuki.bg\/wp-content\/uploads\/2019\/04\/logo-azbuki-e1580374651845.png\",\"contentUrl\":\"https:\/\/azbuki.bg\/wp-content\/uploads\/2019\/04\/logo-azbuki-e1580374651845.png\",\"width\":250,\"height\":70,\"caption\":\"\u0410\u0437-\u0431\u0443\u043a\u0438\"},\"image\":{\"@id\":\"https:\/\/vocedu.azbuki.bg\/en\/#\/schema\/logo\/image\/\"},\"sameAs\":[\"https:\/\/www.facebook.com\/Azbuki55\/\",\"https:\/\/www.instagram.com\/nion_azbuki\/\"]},{\"@type\":\"Person\",\"@id\":\"https:\/\/vocedu.azbuki.bg\/en\/#\/schema\/person\/de220d282eaa494f914ce0fd838645dd\",\"name\":\"\u201e\u0410\u0437-\u0431\u0443\u043a\u0438\u201c\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/vocedu.azbuki.bg\/en\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/d08ccbd951212deb604aa2d403575d4e?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/d08ccbd951212deb604aa2d403575d4e?s=96&d=mm&r=g\",\"caption\":\"\u201e\u0410\u0437-\u0431\u0443\u043a\u0438\u201c\"},\"sameAs\":[\"https:\/\/azbuki.bg\/\"],\"url\":\"https:\/\/strategies.azbuki.bg\/en\/author\/azbuki_ekip\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"\u0413\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0438 \u043c\u0435\u0441\u0442\u0430, \u043f\u043e\u0440\u043e\u0434\u0435\u043d\u0438 \u043e\u0442 \u0440\u0430\u0432\u043d\u043e\u0441\u0442\u0440\u0430\u043d\u043d\u0438 \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u0446\u0438 \u0441 \u0432\u044a\u0440\u0445\u043e\u0432\u0435 \u0432\u044a\u0440\u0445\u0443 \u043e\u043a\u0440\u044a\u0436\u043d\u043e\u0441\u0442 - \u0410\u0437-\u0431\u0443\u043a\u0438","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/pedagogy.azbuki.bg\/en\/uncategorized\/geometrichni-mesta-porodeni-ot-ravnostranni-triagalniczi-s-varhove-varhu-okrazhnost\/","og_locale":"en_US","og_type":"article","og_title":"\u0413\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0438 \u043c\u0435\u0441\u0442\u0430, \u043f\u043e\u0440\u043e\u0434\u0435\u043d\u0438 \u043e\u0442 \u0440\u0430\u0432\u043d\u043e\u0441\u0442\u0440\u0430\u043d\u043d\u0438 \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u0446\u0438 \u0441 \u0432\u044a\u0440\u0445\u043e\u0432\u0435 \u0432\u044a\u0440\u0445\u0443 \u043e\u043a\u0440\u044a\u0436\u043d\u043e\u0441\u0442 - \u0410\u0437-\u0431\u0443\u043a\u0438","og_description":"\u0411\u043e\u0440\u0438\u0441\u043b\u0430\u0432 \u0411\u043e\u0440\u0438\u0441\u043e\u0432, \u0414\u0435\u044f\u043d \u0414\u0438\u043c\u0438\u0442\u0440\u043e\u0432, \u041d\u0438\u043a\u043e\u043b\u0430\u0439 \u041d\u0438\u043d\u043e\u0432, \u0422\u0435\u043e\u0434\u043e\u0440 \u0425\u0440\u0438\u0441\u0442\u043e\u0432 \u041f\u0440\u0438\u0440\u043e\u0434\u043e-\u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0430 \u0433\u0438\u043c\u043d\u0430\u0437\u0438\u044f \u2013 \u041b\u043e\u0432\u0435\u0447 \u0420\u0435\u0437\u044e\u043c\u0435. \u0421\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0435 \u0443\u0447\u0435\u043d\u0438\u0447\u0435\u0441\u043a\u0430 \u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u043a\u0430 \u043f\u043e\u0434 \u0440\u044a\u043a\u043e\u0432\u043e\u0434\u0441\u0442\u0432\u043e\u0442\u043e \u043d\u0430 \u0434\u043e\u0446. \u0434-\u0440 \u0412\u0435\u0441\u0435\u043b\u0438\u043d \u041d\u0435\u043d\u043a\u043e\u0432. \u041d\u043e\u0432\u0438\u0442\u0435 \u0440\u0435\u0437\u0443\u043b\u0442\u0430\u0442\u0438 \u0432 \u043d\u0435\u044f \u043f\u043e\u043b\u0443\u0447\u0438\u0445\u0430 \u043e\u0442\u043b\u0438\u0447\u043d\u0430 \u043e\u0446\u0435\u043d\u043a\u0430 \u043f\u043e \u0432\u0440\u0435\u043c\u0435 \u043d\u0430 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u044f\u043d\u0435\u0442\u043e \u0454 \u0432 \u043c\u0435\u0436\u0434\u0443\u043d\u0430\u0440\u043e\u0434\u043d\u0438\u044f \u043a\u043e\u043d\u043a\u0443\u0440\u0441 \u201e\u041c\u0435\u0442\u043e\u0434\u043e\u043b\u043e\u0433\u0438\u044f \u0438 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u043e\u043d\u043d\u0438 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0438 \u0432 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0435\u0442\u043e\u201c \u043f\u0440\u0435\u0437 2019 \u0433. \u0438 \u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u043a\u0430\u0442\u0430 \u0431\u0435\u0448\u0435 \u0443\u0434\u043e\u0441\u0442\u043e\u0435\u043d\u0430 \u0441 \u043f\u044a\u0440\u0432\u0430 \u043d\u0430\u0433\u0440\u0430\u0434\u0430. [&hellip;]","og_url":"https:\/\/pedagogy.azbuki.bg\/en\/uncategorized\/geometrichni-mesta-porodeni-ot-ravnostranni-triagalniczi-s-varhove-varhu-okrazhnost\/","og_site_name":"\u0410\u0437-\u0431\u0443\u043a\u0438","article_publisher":"https:\/\/www.facebook.com\/Azbuki55\/","article_published_time":"2026-01-29T09:57:11+00:00","author":"\u201e\u0410\u0437-\u0431\u0443\u043a\u0438\u201c","twitter_card":"summary_large_image","twitter_misc":{"Written by":"\u201e\u0410\u0437-\u0431\u0443\u043a\u0438\u201c","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/pedagogy.azbuki.bg\/en\/uncategorized\/geometrichni-mesta-porodeni-ot-ravnostranni-triagalniczi-s-varhove-varhu-okrazhnost\/#article","isPartOf":{"@id":"https:\/\/pedagogy.azbuki.bg\/en\/uncategorized\/geometrichni-mesta-porodeni-ot-ravnostranni-triagalniczi-s-varhove-varhu-okrazhnost\/"},"author":{"name":"\u201e\u0410\u0437-\u0431\u0443\u043a\u0438\u201c","@id":"https:\/\/vocedu.azbuki.bg\/en\/#\/schema\/person\/de220d282eaa494f914ce0fd838645dd"},"headline":"\u0413\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0438 \u043c\u0435\u0441\u0442\u0430, \u043f\u043e\u0440\u043e\u0434\u0435\u043d\u0438 \u043e\u0442 \u0440\u0430\u0432\u043d\u043e\u0441\u0442\u0440\u0430\u043d\u043d\u0438 \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u0446\u0438 \u0441 \u0432\u044a\u0440\u0445\u043e\u0432\u0435 \u0432\u044a\u0440\u0445\u0443 \u043e\u043a\u0440\u044a\u0436\u043d\u043e\u0441\u0442","datePublished":"2026-01-29T09:57:11+00:00","dateModified":"2026-01-29T09:57:11+00:00","mainEntityOfPage":{"@id":"https:\/\/pedagogy.azbuki.bg\/en\/uncategorized\/geometrichni-mesta-porodeni-ot-ravnostranni-triagalniczi-s-varhove-varhu-okrazhnost\/"},"wordCount":164,"publisher":{"@id":"https:\/\/vocedu.azbuki.bg\/en\/#organization"},"keywords":["circle","curve of fourth degree","ellipse","equilateral triangle"],"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/pedagogy.azbuki.bg\/en\/uncategorized\/geometrichni-mesta-porodeni-ot-ravnostranni-triagalniczi-s-varhove-varhu-okrazhnost\/","url":"https:\/\/pedagogy.azbuki.bg\/en\/uncategorized\/geometrichni-mesta-porodeni-ot-ravnostranni-triagalniczi-s-varhove-varhu-okrazhnost\/","name":"\u0413\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0438 \u043c\u0435\u0441\u0442\u0430, \u043f\u043e\u0440\u043e\u0434\u0435\u043d\u0438 \u043e\u0442 \u0440\u0430\u0432\u043d\u043e\u0441\u0442\u0440\u0430\u043d\u043d\u0438 \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u0446\u0438 \u0441 \u0432\u044a\u0440\u0445\u043e\u0432\u0435 \u0432\u044a\u0440\u0445\u0443 \u043e\u043a\u0440\u044a\u0436\u043d\u043e\u0441\u0442 - \u0410\u0437-\u0431\u0443\u043a\u0438","isPartOf":{"@id":"https:\/\/vocedu.azbuki.bg\/en\/#website"},"datePublished":"2026-01-29T09:57:11+00:00","dateModified":"2026-01-29T09:57:11+00:00","breadcrumb":{"@id":"https:\/\/pedagogy.azbuki.bg\/en\/uncategorized\/geometrichni-mesta-porodeni-ot-ravnostranni-triagalniczi-s-varhove-varhu-okrazhnost\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/pedagogy.azbuki.bg\/en\/uncategorized\/geometrichni-mesta-porodeni-ot-ravnostranni-triagalniczi-s-varhove-varhu-okrazhnost\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/pedagogy.azbuki.bg\/en\/uncategorized\/geometrichni-mesta-porodeni-ot-ravnostranni-triagalniczi-s-varhove-varhu-okrazhnost\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/strategies.azbuki.bg\/"},{"@type":"ListItem","position":2,"name":"\u0413\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0438 \u043c\u0435\u0441\u0442\u0430, \u043f\u043e\u0440\u043e\u0434\u0435\u043d\u0438 \u043e\u0442 \u0440\u0430\u0432\u043d\u043e\u0441\u0442\u0440\u0430\u043d\u043d\u0438 \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u0446\u0438 \u0441 \u0432\u044a\u0440\u0445\u043e\u0432\u0435 \u0432\u044a\u0440\u0445\u0443 \u043e\u043a\u0440\u044a\u0436\u043d\u043e\u0441\u0442"}]},{"@type":"WebSite","@id":"https:\/\/vocedu.azbuki.bg\/en\/#website","url":"https:\/\/vocedu.azbuki.bg\/en\/","name":"\u0410\u0437-\u0431\u0443\u043a\u0438","description":"\u041d\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u043d\u043e \u0438\u0437\u0434\u0430\u0442\u0435\u043b\u0441\u0442\u0432\u043e \u0437\u0430 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0435 \u0438 \u043d\u0430\u0443\u043a\u0430","publisher":{"@id":"https:\/\/vocedu.azbuki.bg\/en\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/vocedu.azbuki.bg\/en\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/vocedu.azbuki.bg\/en\/#organization","name":"\u0410\u0437-\u0431\u0443\u043a\u0438","url":"https:\/\/vocedu.azbuki.bg\/en\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/vocedu.azbuki.bg\/en\/#\/schema\/logo\/image\/","url":"https:\/\/azbuki.bg\/wp-content\/uploads\/2019\/04\/logo-azbuki-e1580374651845.png","contentUrl":"https:\/\/azbuki.bg\/wp-content\/uploads\/2019\/04\/logo-azbuki-e1580374651845.png","width":250,"height":70,"caption":"\u0410\u0437-\u0431\u0443\u043a\u0438"},"image":{"@id":"https:\/\/vocedu.azbuki.bg\/en\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.facebook.com\/Azbuki55\/","https:\/\/www.instagram.com\/nion_azbuki\/"]},{"@type":"Person","@id":"https:\/\/vocedu.azbuki.bg\/en\/#\/schema\/person\/de220d282eaa494f914ce0fd838645dd","name":"\u201e\u0410\u0437-\u0431\u0443\u043a\u0438\u201c","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/vocedu.azbuki.bg\/en\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/d08ccbd951212deb604aa2d403575d4e?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/d08ccbd951212deb604aa2d403575d4e?s=96&d=mm&r=g","caption":"\u201e\u0410\u0437-\u0431\u0443\u043a\u0438\u201c"},"sameAs":["https:\/\/azbuki.bg\/"],"url":"https:\/\/strategies.azbuki.bg\/en\/author\/azbuki_ekip\/"}]}},"_links":{"self":[{"href":"https:\/\/strategies.azbuki.bg\/en\/wp-json\/wp\/v2\/posts\/220982"}],"collection":[{"href":"https:\/\/strategies.azbuki.bg\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/strategies.azbuki.bg\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/strategies.azbuki.bg\/en\/wp-json\/wp\/v2\/users\/124332423427287"}],"replies":[{"embeddable":true,"href":"https:\/\/strategies.azbuki.bg\/en\/wp-json\/wp\/v2\/comments?post=220982"}],"version-history":[{"count":1,"href":"https:\/\/strategies.azbuki.bg\/en\/wp-json\/wp\/v2\/posts\/220982\/revisions"}],"predecessor-version":[{"id":220985,"href":"https:\/\/strategies.azbuki.bg\/en\/wp-json\/wp\/v2\/posts\/220982\/revisions\/220985"}],"wp:attachment":[{"href":"https:\/\/strategies.azbuki.bg\/en\/wp-json\/wp\/v2\/media?parent=220982"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/strategies.azbuki.bg\/en\/wp-json\/wp\/v2\/categories?post=220982"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/strategies.azbuki.bg\/en\/wp-json\/wp\/v2\/tags?post=220982"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}