tag:blogger.com,1999:blog-6500033298667240354.post5305699909016879240..comments2024-02-19T00:34:12.578-08:00Comments on Always Creative Geometry Problems plus Occasionally Annoying Philosophy: Fox 2788foxeshttp://www.blogger.com/profile/09567328431908997738noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-6500033298667240354.post-67158602807988735372010-04-30T21:20:02.833-07:002010-04-30T21:20:02.833-07:00Just to complete the formailty: If r is the radius...Just to complete the formailty: If r is the radius of the outer circle then radius of the inner circle = rsin(β/2). The required ratio = ∏(rsin(β/2)^2 /[∏(r)^2 ∏(rsin(β/2)^2] = [tan(β/2)]^2 and [(1-cos(β)]/[(1+cos(β)] can also be shown = [tan(β/2)]^2 by the half angle formula. Hence etc.<br />AjitAjithttps://www.blogger.com/profile/00611759721780927573noreply@blogger.comtag:blogger.com,1999:blog-6500033298667240354.post-30016123713629974262010-04-27T15:22:47.850-07:002010-04-27T15:22:47.850-07:00Sorry that was a typo.Sorry that was a typo.8foxeshttps://www.blogger.com/profile/09567328431908997738noreply@blogger.comtag:blogger.com,1999:blog-6500033298667240354.post-63066741335401698352010-04-27T15:16:41.209-07:002010-04-27T15:16:41.209-07:00Now it is (1-cos)/(1+cos).Now it is (1-cos)/(1+cos).Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6500033298667240354.post-75224926518280313102010-04-27T15:12:48.618-07:002010-04-27T15:12:48.618-07:00(1+cos)/(1-cos)? YU(1+cos)/(1-cos)? YUAnonymousnoreply@blogger.com