tag:blogger.com,1999:blog-6933544261975483399.post6191992612393763608..comments2024-03-26T19:10:02.918-07:00Comments on Go Geometry (Problem Solutions): Geometry Problem 1134: Tangent Circles, Tangent Line, Triangle, Circumcircle, CircumcenterAntonio Gutierrezhttp://www.blogger.com/profile/04521650748152459860noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-6933544261975483399.post-23482590339283624042015-07-14T21:57:20.053-07:002015-07-14T21:57:20.053-07:00Points A ,O1 and O2 are collinear
Lets line joinin...Points A ,O1 and O2 are collinear<br />Lets line joining A,O1 and O2 intersects BD at E and BC at F. <br />Lets assume angle AO2D = x <br />And angle AO1C = y <br />We can see that Angle BEF = 90 - x <br />And Angle BFE = y - 90<br />And we get Angle EBF = Angle DBC = 180 - (y-x) <br /> Also Angle O1AC = 90 - y/2 <br />Angle O1AD = 90 + (x/2) <br />We get angle DAC = 180 - [(y-x)/2] <br />Since O3 is circumcentre of triangle ACD <br />Angle DO3C = y - x <br />It means quad. BCO3D is cyclic and O3 lies on circle O4.Pradyumna Agashehttps://www.blogger.com/profile/10300531209692781145noreply@blogger.com