MathDB

Circles

\omega_1

and

\omega_2

have centres

O_1

and

O_2

, respectively. These two circles intersect at points

X

and

Y

AB

is common tangent line of these two circles such that

A

lies on

\omega_1

and

B

lies on

\omega_2

. Let tangents to

\omega_1

and

\omega_2

X

intersect

O_1O_2

at points

K

and

L

, respectively. Suppose that line

BL

intersects

\omega_2

for the second time at

M

and line

AK

intersects

\omega_1

for the second time at

N

. Prove that lines

AM, BN

and

O_1O_2

concur.
Proposed by Dominik Burek - Poland

Problem Statement