tag:blogger.com,1999:blog-6933544261975483399.post2343882703798117073..comments2023-06-04T15:38:37.025-07:00Comments on Go Geometry (Problem Solutions): Typography of Geometry Problem 1373: Isosceles Triangle, Exterior Cevian, Inradius, Exradius, Altitude, iPad AppsAntonio Gutierrezhttp://www.blogger.com/profile/04521650748152459860noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-6933544261975483399.post-46299158692773544652018-08-04T22:45:57.675-07:002018-08-04T22:45:57.675-07:00Let the in circle be P and the excircle be Q Let D...Let the in circle be P and the excircle be Q<br />Let DAC touch circle P at X &amp; circle Q at Y<br />Let DB touch circle P at U and circle Q at V<br /><br />Let AB = BC = a, AX = b, CY = c and <br />AE = EC = d<br />Let the bisector of &lt; BAE meet BE at T<br /><br />ET = hd / (a + d) ......(1)<br /><br />Now PXA, TEA &amp; QYC are similar triangles<br />So b / r1 = c / r2 = ET / d = h / (a + d) <br />= (b + c) / ( r1 + r2) = (a - d) / (r1 + r2) from (1)<br /><br />Hence (r1 + r2)h = a^2 - d^2 = h^2<br />Therefore r1 + r2 = h<br /><br />Sumith Peiris<br />Moratuwa<br />Sri LankaSumith Peirishttps://www.blogger.com/profile/06211995240466447227noreply@blogger.com