MathDB

Let

\omega_1

and

\omega_2

be two different circles that intersect at two different points,

X

and

Y

. Let lines

l_1

and

l_2

be common tangent lines of these circles such that

l_1

is tangent

\omega_1

A

and

\omega_2

C

and

l_2

is tangent

\omega_1

B

and

\omega_2

D

. Let

Z

be the reflection of

Y

respect to

l_1

and let

BC

and

\omega_1

meet at

K

for the second time. Let

AD

and

\omega_2

meet at

L

for the second time. Prove that the line tangent to

\omega_1

and passes through

K

and the line tangent to

\omega_2

and passes through

L

meet on the line

XZ

Problem Statement