MathDB

13

Part of 2007 Sharygin Geometry Olympiad

Problems(1)

fixed point starting with equal segments on a side of triangle

Source: 2007 Sharygin Geometry Olympiad Correspondence Round P13

4/27/2019
On the side ABAB of a triangle ABCABC, two points X,YX, Y are chosen so that AX=BYAX = BY. Lines CXCX and CYCY meet the circumcircle of the triangle, for the second time, at points UU and VV. Prove that all lines UVUV (for all X,YX, Y, given A,B,CA, B, C) have a common point.
geometryFixed pointcircumcircleequal segments