{"id":221005,"date":"2026-01-29T12:14:54","date_gmt":"2026-01-29T10:14:54","guid":{"rendered":"https:\/\/azbuki.bg\/?p=221005"},"modified":"2026-01-29T12:14:54","modified_gmt":"2026-01-29T10:14:54","slug":"a-triangle-and-a-trapezoid-with-a-common-conic","status":"publish","type":"post","link":"https:\/\/strategies.azbuki.bg\/en\/uncategorized\/a-triangle-and-a-trapezoid-with-a-common-conic\/","title":{"rendered":"A Triangle and a Trapezoid with a Common Conic"},"content":{"rendered":"<p><strong>1) Sava Grozdev, 2) Veselin Nenkov<\/strong><\/p>\n<p><em>1) University of Finance, Business and Entrepreneurship \u2013 Sofia (Bulgaria)<\/em><br \/>\n<em>2) \u201eNikola Vaptsarov\u201c Naval Academy \u2013 Varna (Bulgaria)<\/em><\/p>\n<p><strong>Abstract.<\/strong> The aim of the present note is to propose a generalization of Problem 1 on the IMO\u20192018 paper. The International Mathematical Olympiad (IMO) is the most prestigious scientific Olympiad for high school students. Its 59th edition took place in Cluj-Napoca, Romania, 3\u201314 July 2018. The problem 1 on the paper was solved fully (7 points) by 381 participants, 7 students were marked with 6 points, 7 with 5 points, 10 with 4 points, 15 with 3 points, 24 with 2 points, 54 with 1 point and 96 with 0 points. The mean result of all the 594 participants in the Olympiad from 107 countries is 4, 934, which shows that the problem is easy and has not bordered most of the contestants. Nevertheless it turns out to be interesting and originates rich in content ideas.<\/p>\n<p><em>Keywords:<\/em> Olympiad; problem solving; triangle; trapezoid; conic<\/p>\n<p><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2026\/01\/math_info_2_19_grozdev_nenkov.pdf\">>> Download the article as a PDF file <<<\/a><\/p>","protected":false},"excerpt":{"rendered":"<p>1) Sava Grozdev, 2) Veselin Nenkov 1) University of Finance, Business and Entrepreneurship \u2013 Sofia (Bulgaria) 2) \u201eNikola Vaptsarov\u201c Naval Academy \u2013 Varna (Bulgaria) Abstract. The aim of the present note is to propose a generalization of Problem 1 on the IMO\u20192018 paper. The International Mathematical Olympiad (IMO) is the most prestigious scientific Olympiad for [&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":[16090,16180,16181,16182,16088],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>A Triangle and a Trapezoid with a Common Conic - \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:\/\/bel.azbuki.bg\/uncategorized\/a-triangle-and-a-trapezoid-with-a-common-conic\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A Triangle and a Trapezoid with a Common Conic - \u0410\u0437-\u0431\u0443\u043a\u0438\" \/>\n<meta property=\"og:description\" content=\"1) Sava Grozdev, 2) Veselin Nenkov 1) University of Finance, Business and Entrepreneurship \u2013 Sofia (Bulgaria) 2) \u201eNikola Vaptsarov\u201c Naval Academy \u2013 Varna (Bulgaria) Abstract. The aim of the present note is to propose a generalization of Problem 1 on the IMO\u20192018 paper. The International Mathematical Olympiad (IMO) is the most prestigious scientific Olympiad for [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/bel.azbuki.bg\/uncategorized\/a-triangle-and-a-trapezoid-with-a-common-conic\/\" \/>\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=\"2026-01-29T10:14:54+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:\/\/bel.azbuki.bg\/uncategorized\/a-triangle-and-a-trapezoid-with-a-common-conic\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/bel.azbuki.bg\/uncategorized\/a-triangle-and-a-trapezoid-with-a-common-conic\/\"},\"author\":{\"name\":\"\u201e\u0410\u0437-\u0431\u0443\u043a\u0438\u201c\",\"@id\":\"https:\/\/vocedu.azbuki.bg\/en\/#\/schema\/person\/de220d282eaa494f914ce0fd838645dd\"},\"headline\":\"A Triangle and a Trapezoid with a Common Conic\",\"datePublished\":\"2026-01-29T10:14:54+00:00\",\"dateModified\":\"2026-01-29T10:14:54+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/bel.azbuki.bg\/uncategorized\/a-triangle-and-a-trapezoid-with-a-common-conic\/\"},\"wordCount\":154,\"publisher\":{\"@id\":\"https:\/\/vocedu.azbuki.bg\/en\/#organization\"},\"keywords\":[\"conic\",\"Olympiad\",\"problem solving\",\"trapezoid\",\"triangle\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/bel.azbuki.bg\/uncategorized\/a-triangle-and-a-trapezoid-with-a-common-conic\/\",\"url\":\"https:\/\/bel.azbuki.bg\/uncategorized\/a-triangle-and-a-trapezoid-with-a-common-conic\/\",\"name\":\"A Triangle and a Trapezoid with a Common Conic - 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