tag:blogger.com,1999:blog-6933544261975483399.post7383274249874864254..comments2024-03-26T19:10:02.918-07:00Comments on Go Geometry (Problem Solutions): Geometry Problem 1066: Triangle, Obtuse Angle, Orthocenter, Circumradius, Inradius, Exradius, Distance, DiameterAntonio Gutierrezhttp://www.blogger.com/profile/04521650748152459860noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-6933544261975483399.post-21259863101561820802014-12-04T16:00:59.781-08:002014-12-04T16:00:59.781-08:00Since ΔABC and ΔHBC have the same circumradius,
a...Since ΔABC and ΔHBC have the same circumradius, <br />a₁ = 2R cosH = −2R cosA<br />r = 4R sin(A/2) sin(B/2) sin(C/2)<br />r₁ = 4R sin(A/2) cos(B/2) cos(C/2)<br /><br />r₁ − r = 4R sin(A/2) cos(B/2 + C/2) <br />= 4R sin²(A/2) = 2R(1−cosA) = 2R + a₁<br />a₁ + r₁ − r = 2R<br />r₁ − a₁ = 2R + rJacob HA (EMK2000)https://www.blogger.com/profile/17238561555526381028noreply@blogger.com