{"id":220988,"date":"2026-01-29T12:01:47","date_gmt":"2026-01-29T10:01:47","guid":{"rendered":"https:\/\/azbuki.bg\/?p=220988"},"modified":"2026-01-29T12:30:57","modified_gmt":"2026-01-29T10:30:57","slug":"one-generalization-of-the-geometric-problem-from-19th-junior-balkan-mathematical-olympiad","status":"publish","type":"post","link":"https:\/\/bel.azbuki.bg\/en\/uncategorized\/one-generalization-of-the-geometric-problem-from-19th-junior-balkan-mathematical-olympiad\/","title":{"rendered":"One Generalization of the Geometric Problem from 19th Junior Balkan Mathematical Olympiad"},"content":{"rendered":"<p><strong>1) Ivaylo Staribratov, 2) Radka Todorova<\/strong><\/p>\n<p><em>1) University of Plovdiv \u201cPaisii Hilendarski\u201d (Bulgaria)<\/em><br \/>\n<em>2) Mathematical School \u201cAcademic Kiril Popov\u201d \u2013 Plovdiv (Bulgaria)<\/em><\/p>\n<p><strong>Abstract.<\/strong> We present one possible generalization, inspired by the usage of the Dynamic Geometry Software GeoGebra, of the geometric problem from the 19th Junior Balkan Mathematical Olympiad. We have presented the process of the generalization in front of students about 16 \u2013 17 years of age from the Mathematical School \u201cAcademic Kiril Popov\u201d \u2013 Plovdiv. We have use the technique of tree diagrams to ease students\u2019 understanding of the solution and to help them in the steps of the generalization.<\/p>\n<p><em>Keywords:<\/em> Math Olympiad; Dynamic geometry software; Experiment; Tree diagram<\/p>\n<p><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2026\/01\/math_info_2_19_staribratov_todorova.pdf\">>> Download the article as a PDF file <<<\/a><\/p>","protected":false},"excerpt":{"rendered":"<p>1) Ivaylo Staribratov, 2) Radka Todorova 1) University of Plovdiv \u201cPaisii Hilendarski\u201d (Bulgaria) 2) Mathematical School \u201cAcademic Kiril Popov\u201d \u2013 Plovdiv (Bulgaria) Abstract. We present one possible generalization, inspired by the usage of the Dynamic Geometry Software GeoGebra, of the geometric problem from the 19th Junior Balkan Mathematical Olympiad. We have presented the process of [&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":[16169,16170,16168,16171],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>One Generalization of the Geometric Problem from 19th Junior Balkan Mathematical Olympiad - \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:\/\/vocedu.azbuki.bg\/uncategorized\/one-generalization-of-the-geometric-problem-from-19th-junior-balkan-mathematical-olympiad\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"One Generalization of the Geometric Problem from 19th Junior Balkan Mathematical Olympiad - \u0410\u0437-\u0431\u0443\u043a\u0438\" \/>\n<meta property=\"og:description\" content=\"1) Ivaylo Staribratov, 2) Radka Todorova 1) University of Plovdiv \u201cPaisii Hilendarski\u201d (Bulgaria) 2) Mathematical School \u201cAcademic Kiril Popov\u201d \u2013 Plovdiv (Bulgaria) Abstract. We present one possible generalization, inspired by the usage of the Dynamic Geometry Software GeoGebra, of the geometric problem from the 19th Junior Balkan Mathematical Olympiad. We have presented the process of [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/vocedu.azbuki.bg\/uncategorized\/one-generalization-of-the-geometric-problem-from-19th-junior-balkan-mathematical-olympiad\/\" \/>\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=\"2026-01-29T10:01:47+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2026-01-29T10:30:57+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:\/\/vocedu.azbuki.bg\/uncategorized\/one-generalization-of-the-geometric-problem-from-19th-junior-balkan-mathematical-olympiad\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/vocedu.azbuki.bg\/uncategorized\/one-generalization-of-the-geometric-problem-from-19th-junior-balkan-mathematical-olympiad\/\"},\"author\":{\"name\":\"\u201e\u0410\u0437-\u0431\u0443\u043a\u0438\u201c\",\"@id\":\"https:\/\/vocedu.azbuki.bg\/en\/#\/schema\/person\/de220d282eaa494f914ce0fd838645dd\"},\"headline\":\"One Generalization of the Geometric Problem from 19th Junior Balkan Mathematical Olympiad\",\"datePublished\":\"2026-01-29T10:01:47+00:00\",\"dateModified\":\"2026-01-29T10:30:57+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/vocedu.azbuki.bg\/uncategorized\/one-generalization-of-the-geometric-problem-from-19th-junior-balkan-mathematical-olympiad\/\"},\"wordCount\":122,\"publisher\":{\"@id\":\"https:\/\/vocedu.azbuki.bg\/en\/#organization\"},\"keywords\":[\"Dynamic geometry software\",\"Experiment\",\"Math Olympiad\",\"Tree diagram\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/vocedu.azbuki.bg\/uncategorized\/one-generalization-of-the-geometric-problem-from-19th-junior-balkan-mathematical-olympiad\/\",\"url\":\"https:\/\/vocedu.azbuki.bg\/uncategorized\/one-generalization-of-the-geometric-problem-from-19th-junior-balkan-mathematical-olympiad\/\",\"name\":\"One Generalization of the Geometric Problem from 19th Junior Balkan Mathematical Olympiad - 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