{"id":216,"date":"2019-01-25T14:30:20","date_gmt":"2019-01-25T20:30:20","guid":{"rendered":"http:\/\/blogs.acu.edu\/mu_sigma\/?p=216"},"modified":"2019-02-01T15:18:26","modified_gmt":"2019-02-01T21:18:26","slug":"problem-10","status":"publish","type":"post","link":"https:\/\/blogs.acu.edu\/mu_sigma\/2019\/01\/25\/problem-10\/","title":{"rendered":"Problem 10 &#8211; Find the Angle &#8211; January 25, 2019"},"content":{"rendered":"<h2><b>Find the Angle<\/b><\/h2>\n<p>Refer to the figure below. A circle of radius 1 is tangent to a circle of radius 3. The segment <b>OA<\/b> passes through the centers of the circles. The segment <b>OB<\/b> is tangent to both circles. Find the degree measurement of the angle <b>AOB<\/b>.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/math.acu.edu\/green\/pow\/20031\/pow01fig.gif\" width=\"386\" height=\"303\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>Submit your answers to mathpotw@acu.edu. \u00a0Details for submissions can be found\u00a0<a href=\"http:\/\/blogs.acu.edu\/mu_sigma\/2018\/08\/28\/problem-of-the-week-competition\/\">here<\/a>.<\/p>\n<p><span style=\"font-size: large\">Solution to <b>Find the Angle<\/b><\/span><\/p>\n<p><span style=\"font-size: small\"><i>Correct solutions were submitted by: \u00a0Yunxi Wei, Wyatt Witemeyer, Bethany Witemeyer<\/i><\/span><\/p>\n<p>In the figure below, the length of the segment from <i>D<\/i> to <i>F<\/i> is 1 and the length of the segment from <i>E<\/i> to <i>G<\/i> is 3. If the distance from <i>O<\/i> to <i>D<\/i> is <i>x<\/i> then the distance from <i>O<\/i> to <i>E<\/i> is <i>x<\/i>+4. From similar triangles we see that <i>x<\/i> is to 1 as <i>x<\/i>+4 is to 3. Solving this equation gives <i>x<\/i> = 2. Therefore the sine of the angle in question is 1\/2, making the angle itself have 30 degrees.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/math.acu.edu\/green\/pow\/20031\/sol01im1.gif\" width=\"400\" height=\"303\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Find the Angle Refer to the figure below. A circle of radius 1 is tangent to a circle of radius 3. The segment OA passes through the centers of the circles. The segment OB is tangent to both circles. Find the degree measurement of the angle AOB. &nbsp; Submit your answers to mathpotw@acu.edu. \u00a0Details for [&hellip;]<\/p>\n","protected":false},"author":130,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"","_et_pb_old_content":"","_et_gb_content_width":"","footnotes":""},"categories":[181534],"tags":[],"class_list":["post-216","post","type-post","status-publish","format-standard","hentry","category-problem-of-the-week"],"_links":{"self":[{"href":"https:\/\/blogs.acu.edu\/mu_sigma\/wp-json\/wp\/v2\/posts\/216","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.acu.edu\/mu_sigma\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.acu.edu\/mu_sigma\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.acu.edu\/mu_sigma\/wp-json\/wp\/v2\/users\/130"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.acu.edu\/mu_sigma\/wp-json\/wp\/v2\/comments?post=216"}],"version-history":[{"count":4,"href":"https:\/\/blogs.acu.edu\/mu_sigma\/wp-json\/wp\/v2\/posts\/216\/revisions"}],"predecessor-version":[{"id":224,"href":"https:\/\/blogs.acu.edu\/mu_sigma\/wp-json\/wp\/v2\/posts\/216\/revisions\/224"}],"wp:attachment":[{"href":"https:\/\/blogs.acu.edu\/mu_sigma\/wp-json\/wp\/v2\/media?parent=216"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.acu.edu\/mu_sigma\/wp-json\/wp\/v2\/categories?post=216"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.acu.edu\/mu_sigma\/wp-json\/wp\/v2\/tags?post=216"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}