{"id":1980,"date":"2021-01-16T09:53:39","date_gmt":"2021-01-16T14:53:39","guid":{"rendered":"http:\/\/josmfs.net\/?p=1980"},"modified":"2021-01-16T09:53:39","modified_gmt":"2021-01-16T14:53:39","slug":"twin-intersection-puzzle","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2021\/01\/16\/twin-intersection-puzzle\/","title":{"rendered":"Twin Intersection Puzzle"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-1978\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/01\/Twin-Intersection-Puzzle-Fig2.jpg\" alt=\"\" width=\"213\" height=\"163\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/01\/Twin-Intersection-Puzzle-Fig2.jpg 368w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/01\/Twin-Intersection-Puzzle-Fig2-300x230.jpg 300w\" sizes=\"auto, (max-width: 213px) 100vw, 213px\" \/>This is an interesting problem from the 1977 Canadian Math Society\u2019s magazine, <em>Crux Mathematicorum<\/em>.<\/p>\n<p>\u201c206. [1977: 10] <em>Proposed by Dan Pedoe, University of Minnesota.<\/em><\/p>\n<p>A circle intersects the sides BC, CA and AB of a triangle ABC in the pairs of points X, X&#8217;, Y, Y&#8217; and Z, Z&#8217; respectively. If the perpendiculars at X, Y and Z to the respective sides BC, CA and AB are concurrent at a point P, prove that the respective perpendiculars at X&#8217;, Y&#8217; and Z&#8217; to the sides BC, CA and AB are concurrent at a point P&#8217;.\u201d<\/p>\n<p>See the <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/01\/Twin-Intersection-Puzzle-210106.pdf\">Twin Intersection Puzzle<\/a><\/p>\n<p>Puzzles and Problems: plane geometry, Dan Pedoe, Crux Mathematicorum<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This is an interesting problem from the 1977 Canadian Math Society\u2019s magazine, Crux Mathematicorum. \u201c206. [1977: 10] Proposed by Dan Pedoe, University of Minnesota. A circle intersects the sides BC, CA and AB of a triangle ABC in the pairs of points X, X&#8217;, Y, Y&#8217; and Z, Z&#8217; respectively. If the perpendiculars at X, [&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":[212,211,13],"class_list":["post-1980","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-crux-mathematicorum","tag-dan-pedoe","tag-plane-geometry"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1980","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=1980"}],"version-history":[{"count":1,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1980\/revisions"}],"predecessor-version":[{"id":1981,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1980\/revisions\/1981"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=1980"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=1980"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=1980"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}