{"id":4030,"date":"2024-07-27T10:12:56","date_gmt":"2024-07-27T14:12:56","guid":{"rendered":"https:\/\/josmfs.net\/?p=4030"},"modified":"2024-07-27T12:20:32","modified_gmt":"2024-07-27T16:20:32","slug":"parallel-lines-problem","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2024\/07\/27\/parallel-lines-problem\/","title":{"rendered":"Parallel Lines Problem"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-4028\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/07\/Parallel-Lines-Problem-Fig2.jpg\" alt=\"\" width=\"200\" height=\"213\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/07\/Parallel-Lines-Problem-Fig2.jpg 462w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/07\/Parallel-Lines-Problem-Fig2-282x300.jpg 282w\" sizes=\"auto, (max-width: 200px) 100vw, 200px\" \/>This is an interesting problem from the collection <em>Five Hundred Mathematical Challenges<\/em>.<\/p>\n<p><strong>\u201cProblem 251.<\/strong>\u00a0 Let <em>ABCD <\/em>be a square, <em>F <\/em>be the midpoint of<em> DC<\/em>, and <em>E <\/em>be any point on <em>AB <\/em>such that <em>AE <\/em>&gt; <em>EB<\/em>.\u00a0 Determine <em>N <\/em>on <em>BC <\/em>such that <em>DE <\/em>|| <em>FN<\/em>.\u00a0 Prove that <em>EN <\/em>is tangent to the inscribed circle of the square.\u201d<\/p>\n<p>See the <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/07\/Parallel-Lines-Problem-240313.pdf\">Parallel Lines Problem<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This is an interesting problem from the collection Five Hundred Mathematical Challenges. \u201cProblem 251.\u00a0 Let ABCD be a square, F be the midpoint of DC, and E be any point on AB such that AE &gt; EB.\u00a0 Determine N on BC such that DE || FN.\u00a0 Prove that EN is tangent to the inscribed circle [&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":[177,40],"class_list":["post-4030","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-500-math-challenges","tag-analytic-geometry"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/4030","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=4030"}],"version-history":[{"count":1,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/4030\/revisions"}],"predecessor-version":[{"id":4031,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/4030\/revisions\/4031"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=4030"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=4030"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=4030"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}