{"id":1544,"date":"2020-04-04T13:22:55","date_gmt":"2020-04-04T17:22:55","guid":{"rendered":"http:\/\/josmfs.net\/?p=1544"},"modified":"2024-04-09T14:51:18","modified_gmt":"2024-04-09T18:51:18","slug":"circle-in-slot-problem","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2020\/04\/04\/circle-in-slot-problem\/","title":{"rendered":"Circle in Slot Problem"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft size-full wp-image-1542\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2020\/04\/Circle-in-Slot-Prob-Fig.jpg\" alt=\"\" width=\"201\" height=\"117\" \/>Here is another UKMT Senior Challenge problem from 2017, which has a straight-forward solution:<\/p>\n<p>\u201cThe diagram shows a circle of radius 1 touching three sides of a 2 x 4 rectangle. A diagonal of the rectangle intersects the circle at P and Q, as shown.<\/p>\n<p>What is the length of the chord PQ?<\/p>\n<p><span style=\"color: #ffffff;\">__<\/span>A<span style=\"color: #ffffff;\">_<\/span>\u221a5<span style=\"color: #ffffff;\">____<\/span>B<span style=\"color: #ffffff;\">_<\/span>4\/\u221a5<span style=\"color: #ffffff;\">____<\/span>C<span style=\"color: #ffffff;\">_<\/span>\u221a5 \u2013 2\/\u221a5<span style=\"color: #ffffff;\">____<\/span>D<span style=\"color: #ffffff;\">_<\/span>5\u221a5\/6<span style=\"color: #ffffff;\">____<\/span>E<span style=\"color: #ffffff;\">_<\/span>2\u201d<\/p>\n<p><a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/04\/Circle-in-Slot-Answer.jpg\">Answer<\/a>.<\/p>\n<p>See the <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2020\/04\/Circle-in-Slot-Problem-190902.pdf\">Circle in Slot Problem<\/a> for a solution.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Here is another UKMT Senior Challenge problem from 2017, which has a straight-forward solution: \u201cThe diagram shows a circle of radius 1 touching three sides of a 2 x 4 rectangle. A diagonal of the rectangle intersects the circle at P and Q, as shown. What is the length of the chord PQ? __A_\u221a5____B_4\/\u221a5____C_\u221a5 \u2013 [&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":[13,83],"class_list":["post-1544","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-plane-geometry","tag-ukmt-challenge"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1544","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=1544"}],"version-history":[{"count":2,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1544\/revisions"}],"predecessor-version":[{"id":3767,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1544\/revisions\/3767"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=1544"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=1544"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=1544"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}