{"id":4244,"date":"2025-01-25T09:25:09","date_gmt":"2025-01-25T14:25:09","guid":{"rendered":"https:\/\/josmfs.net\/?p=4244"},"modified":"2025-01-25T09:25:09","modified_gmt":"2025-01-25T14:25:09","slug":"ubiquitous-60-degree-problem","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2025\/01\/25\/ubiquitous-60-degree-problem\/","title":{"rendered":"Ubiquitous 60 Degree Problem"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-4242\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2025\/01\/Ubiquitous-60-Deg-Prob-Fig2.jpg\" alt=\"\" width=\"249\" height=\"163\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2025\/01\/Ubiquitous-60-Deg-Prob-Fig2.jpg 500w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2025\/01\/Ubiquitous-60-Deg-Prob-Fig2-300x196.jpg 300w\" sizes=\"auto, (max-width: 249px) 100vw, 249px\" \/>This is an interesting problem from the Canadian Mathematical Society\u2019s 2001 <em>Olymon<\/em>.<\/p>\n<p>\u201cSuppose that <em>XTY<\/em> is a straight line and that <em>TU<\/em> and <em>TV<\/em> are two rays emanating from <em>T<\/em> for which <em>XTU<\/em> = <em>UTV<\/em> = <em>VTY<\/em> = 60\u00ba. Suppose that <em>P<\/em>, <em>Q<\/em> and <em>R<\/em> are respective points on the rays <em>TY, TU<\/em> and <em>TV<\/em> for which <em>PQ = PR<\/em>. Prove that <em>QPR<\/em> = 60\u00ba.\u201d<\/p>\n<p>See the <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2025\/01\/Ubiquitous-60-Deg-Prob-240403.pdf\">Ubiquitous 60 Degree Problem<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This is an interesting problem from the Canadian Mathematical Society\u2019s 2001 Olymon. \u201cSuppose that XTY is a straight line and that TU and TV are two rays emanating from T for which XTU = UTV = VTY = 60\u00ba. Suppose that P, Q and R are respective points on the rays TY, TU and TV [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[205,13],"class_list":["post-4244","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-ed-barbeau","tag-plane-geometry"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/4244","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=4244"}],"version-history":[{"count":1,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/4244\/revisions"}],"predecessor-version":[{"id":4245,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/4244\/revisions\/4245"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=4244"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=4244"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=4244"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}