MathDB

Let

M

be the intersection point of the diagonals of the parallelogram

ABCD

. Consider three circles passing through

M

, the first and second touch

AB

at points

A

and

B

, respectively, and the third passes through

C

and

D

. Let us denote by

P

and

C

, respectively, the intersection points of the first circle with the third and the second with the third, different from

M

. Prove that the line

PQ

touches the first and second circles.

Problem Statement