{"id":3082,"date":"2023-02-18T07:16:18","date_gmt":"2023-02-18T12:16:18","guid":{"rendered":"https:\/\/josmfs.net\/?p=3082"},"modified":"2023-06-09T12:51:12","modified_gmt":"2023-06-09T16:51:12","slug":"linked-triangles-problem","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2023\/02\/18\/linked-triangles-problem\/","title":{"rendered":"Linked Triangles Problem"},"content":{"rendered":"

\"\"I found this problem from the 1981 Canadian Math Society\u2019s magazine, Crux Mathematicorum<\/em>, to be quite challenging.<\/p>\n

\u201cProposed by Kaidy Tan, Fukien Teachers\u2019 University, Foochow, Fukien, China.<\/em><\/p>\n

An isosceles triangle has vertex A and base BC. Through a point F on AB, a perpendicular to AB is drawn to meet AC in E and BC produced in D. Prove synthetically that<\/p>\n

Area of AFE = 2 Area of CDE \u00a0\u00a0if and only if\u00a0 AF = CD.\u201d<\/p>\n

See the Linked Triangles Problem<\/a><\/p>\n

(Update 2\/22\/2023, 6\/9\/2023) Alternative Solutions<\/strong><\/p>\n

<\/p>\n

(Update 2\/22\/2023)<\/strong><\/p>\n

The indefatigable Oscar Rojas has come up with an alternative solution to the problem. It takes a bit of study to verify.<\/p>\n

\"\"<\/p>\n

(Update 6\/9\/2023)<\/strong><\/p>\n

Srhiri Noe from Morocco, a former high school teacher and teacher trainer, has provided another solution to the problem.\u00a0 I have edited the solution slightly for clarity.<\/p>\n

\"\"<\/p>\n","protected":false},"excerpt":{"rendered":"

I found this problem from the 1981 Canadian Math Society\u2019s magazine, Crux Mathematicorum, to be quite challenging. \u201cProposed by Kaidy Tan, Fukien Teachers\u2019 University, Foochow, Fukien, China. An isosceles triangle has vertex A and base BC. Through a point F on AB, a perpendicular to AB is drawn to meet AC in E and BC […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[212,13],"class_list":["post-3082","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-crux-mathematicorum","tag-plane-geometry"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/3082","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/comments?post=3082"}],"version-history":[{"count":4,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/3082\/revisions"}],"predecessor-version":[{"id":3200,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/3082\/revisions\/3200"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=3082"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=3082"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=3082"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}