{"id":3098,"date":"2023-03-04T12:25:44","date_gmt":"2023-03-04T17:25:44","guid":{"rendered":"https:\/\/josmfs.net\/?p=3098"},"modified":"2023-03-04T15:16:15","modified_gmt":"2023-03-04T20:16:15","slug":"line-work","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2023\/03\/04\/line-work\/","title":{"rendered":"Line Work"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-3096\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/03\/Line-Work-Fig2.jpg\" alt=\"\" width=\"200\" height=\"131\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/03\/Line-Work-Fig2.jpg 503w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/03\/Line-Work-Fig2-300x197.jpg 300w\" sizes=\"auto, (max-width: 200px) 100vw, 200px\" \/>This is a fairly simple problem from <a href=\"https:\/\/www.futilitycloset.com\/2022\/03\/26\/line-work-2\/\">Futility Closet<\/a>, which is currently under a hiatus.<\/p>\n<p>\u201cRobert Bilinski proposed this problem in the April 2006 issue of <em>Crux Mathematicorum<\/em>. On square <em>ABCD<\/em>, two equilateral triangles are constructed, <em>ABE<\/em> internally and <em>BCF<\/em> externally, as shown. Prove that <em>D<\/em>, <em>E<\/em>, and <em>F<\/em> are collinear.\u201d<\/p>\n<p>See <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/03\/Line-Work-220326.pdf\">Line Work<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This is a fairly simple problem from Futility Closet, which is currently under a hiatus. \u201cRobert Bilinski proposed this problem in the April 2006 issue of Crux Mathematicorum. On square ABCD, two equilateral triangles are constructed, ABE internally and BCF externally, as shown. Prove that D, E, and F are collinear.\u201d See Line Work<\/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":[212,16,13],"class_list":["post-3098","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-crux-mathematicorum","tag-futility-closet","tag-plane-geometry"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/3098","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=3098"}],"version-history":[{"count":4,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/3098\/revisions"}],"predecessor-version":[{"id":3104,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/3098\/revisions\/3104"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=3098"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=3098"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=3098"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}