MathDB

Let

\omega_1,\omega_2

be two circles with centers

O_1

and

O_2

, respectively. These two circles intersect each other at points

A

and

B

. Line

O_1B

intersects

\omega_2

for the second time at point

C

, and line

O_2A

intersects

\omega_1

for the second time at point

D

. Let

X

be the second intersection of

AC

and

\omega_1

. Also

Y

is the second intersection point of

BD

and

\omega_2

. Prove that

CX = DY

.
Proposed by Alireza Dadgarnia

Problem Statement