{"id":2924,"date":"2022-10-22T08:08:45","date_gmt":"2022-10-22T12:08:45","guid":{"rendered":"https:\/\/josmfs.net\/?p=2924"},"modified":"2024-04-06T10:03:49","modified_gmt":"2024-04-06T14:03:49","slug":"road-construction-problem","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2022\/10\/22\/road-construction-problem\/","title":{"rendered":"Road Construction Problem"},"content":{"rendered":"

\"\"This is an interesting problem from the Scottish Mathematics Council (SMC) 2014 Senior\u00a0 Math Challenge .<\/p>\n

\u201cTwo straight sections of a road, each running from east to west, and located as shown, are to be joined smoothly by a new roadway consisting of arcs of two circles of equal radius. The existing roads are to be tangents at the joins and the arcs themselves are to have a common tangent where they meet. \u00a0Find the length of the radius of these arcs.\u201d<\/p>\n

Answer<\/a>.<\/p>\n

See the Road Construction Problem<\/a> for solutions.<\/p>\n","protected":false},"excerpt":{"rendered":"

This is an interesting problem from the Scottish Mathematics Council (SMC) 2014 Senior\u00a0 Math Challenge . \u201cTwo straight sections of a road, each running from east to west, and located as shown, are to be joined smoothly by a new roadway consisting of arcs of two circles of equal radius. The existing roads are to […]<\/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":[13,221],"class_list":["post-2924","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-plane-geometry","tag-smc-challenge"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2924","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=2924"}],"version-history":[{"count":4,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2924\/revisions"}],"predecessor-version":[{"id":3591,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2924\/revisions\/3591"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=2924"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=2924"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=2924"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}