{"id":1378,"date":"2019-12-15T07:51:33","date_gmt":"2019-12-15T12:51:33","guid":{"rendered":"http:\/\/josmfs.net\/?p=1378"},"modified":"2019-12-15T08:02:06","modified_gmt":"2019-12-15T13:02:06","slug":"magic-hexagons","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2019\/12\/15\/magic-hexagons\/","title":{"rendered":"Magic Hexagons"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft size-full wp-image-1376\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2019\/12\/Magic-Hexagons-Fig.jpg\" alt=\"\" width=\"300\" height=\"163\" \/>This is truly an amazing result from <em>Five Hundred Mathematical Challenges<\/em>.<\/p>\n<p>\u201c<strong>Problem 119<\/strong>. Two unequal regular hexagons ABCDEF and CGHJKL touch each other at C and are so situated that F, C, and J are collinear.<\/p>\n<p>Show that<\/p>\n<p style=\"text-align: left; padding-left: 160px;\">(i) the circumcircle of BCG bisects FJ (at O say);<br \/>\n(ii) \u0394BOG is equilateral.\u201d<\/p>\n<p>I wonder how anyone ever discovered this.<\/p>\n<p>See the <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2019\/12\/Magic-Hexagons-191127.pdf\">Magic Hexagons<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This is truly an amazing result from Five Hundred Mathematical Challenges. \u201cProblem 119. Two unequal regular hexagons ABCDEF and CGHJKL touch each other at C and are so situated that F, C, and J are collinear. Show that (i) the circumcircle of BCG bisects FJ (at O say); (ii) \u0394BOG is equilateral.\u201d I wonder how [&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":[177,40,13],"class_list":["post-1378","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-500-math-challenges","tag-analytic-geometry","tag-plane-geometry"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1378","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=1378"}],"version-history":[{"count":5,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1378\/revisions"}],"predecessor-version":[{"id":1384,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1378\/revisions\/1384"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=1378"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=1378"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=1378"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}