{"id":1035,"date":"2019-05-29T12:45:21","date_gmt":"2019-05-29T16:45:21","guid":{"rendered":"http:\/\/josmfs.net\/?p=1035"},"modified":"2024-04-10T18:11:02","modified_gmt":"2024-04-10T22:11:02","slug":"rising-sun","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2019\/05\/29\/rising-sun\/","title":{"rendered":"Rising Sun"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-2212\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/06\/Rising-Sun-Fig2.jpg\" alt=\"\" width=\"250\" height=\"100\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/06\/Rising-Sun-Fig2.jpg 500w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/06\/Rising-Sun-Fig2-300x120.jpg 300w\" sizes=\"auto, (max-width: 250px) 100vw, 250px\" \/>Here is a problem from the UKMT Senior (17-18 year-old) Mathematics Challenge for 2012:<\/p>\n<p>\u201cA semicircle of radius r is drawn with centre V and diameter UW. The line UW is then extended to the point X, such that UW and WX are of equal length. An arc of the circle with centre X and radius 4r is then drawn so that the line XY is tangent to the semicircle at Z, as shown. What, in terms of r, is the area of triangle YVW?\u201d<\/p>\n<p><a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/04\/Rising-Sun-Answer.jpg\">Answer<\/a>.<\/p>\n<p>See the <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2019\/05\/Rising-Sun-190413.pdf\">Rising Sun<\/a> for solutions.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Here is a problem from the UKMT Senior (17-18 year-old) Mathematics Challenge for 2012: \u201cA semicircle of radius r is drawn with centre V and diameter UW. The line UW is then extended to the point X, such that UW and WX are of equal length. An arc of the circle with centre X and [&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-1035","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\/1035","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=1035"}],"version-history":[{"count":3,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1035\/revisions"}],"predecessor-version":[{"id":3831,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1035\/revisions\/3831"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=1035"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=1035"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=1035"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}