MathDB

Three circles

\omega_1

\omega_2

and

\omega_3

pass through one common point, say

P

. The tangent line to

\omega_1

P

intersects

\omega_2

and

\omega_3

for the second time at points

P_{1,2}

and

P_{1,3}

, respectively. Points

P_{2,1}

P_{2,3}

P_{3,1}

and

P_{3,2}

are similarly defined. Prove that the perpendicular bisector of segments

P_{1,2}P_{1,3}

P_{2,1}P_{2,3}

and

P_{3,1}P_{3,2}

are concurrent.
Proposed by Mahdi Etesamifard

Problem Statement