MathDB
A property of touching circles

Source: CWMO P2

August 20, 2015
geometryangle bisector

Problem Statement

Two circles (Ω1),(Ω2) \left(\Omega_1\right),\left(\Omega_2\right) touch internally on the point T T . Let M,N M,N be two points on the circle (Ω1) \left(\Omega_1\right) which are different from T T and A,B,C,D A,B,C,D be four points on (Ω2) \left(\Omega_2\right) such that the chords AB,CD AB, CD pass through M,N M,N , respectively. Prove that if AC,BD,MN AC,BD,MN have a common point K K , then TK TK is the angle bisector of MTN \angle MTN .
* (Ω2) \left(\Omega_2\right) is bigger than (Ω1) \left(\Omega_1\right)