MathDB

Two equal circles

\Omega_1

and

\Omega_2

intersect at points

A

and

B

, and

M

is the midpoint of

AB

. Two rays were drawn from

M

, lying in the same half-plane wrt

AB

(see figure). The first ray intersects the circles

\Omega_1

and

\Omega_2

at points

X_1

and

X_2

, and the second ray intersects them at points

Y_1

and

Y_2

, respectively. Let

C

be the intersection point of straight lines

AX_1

and

BY_2

, and let

D

be the intersection point of straight lines

AX_2

and

BY_1

. Prove that

CD \parallel AB

. https://cdn.artofproblemsolving.com/attachments/4/a/fae047c3956d8b30f15a9d88e8d12e5f4d48ec.png

Problem Statement