fixed point's revenge, 4 circles related, tangent circles related
Source: Ukraine TST 2009 p8
May 2, 2020
geometryFixed pointcirclestangent circlesfixed
Problem Statement
Two circles are given, with centers at points respectively. Select a point on circle and construct two circles, one that touches circle at point and circle at a point , and the other that touches circle at point and circle at a point . Prove that, regardless of the choice of point K on circle , all lines pass through a fixed point of the plane.