MathDB

Consider an isosceles triangle

ABC

with

AB=AC

, and a circle

\omega

which is tangent to the sides

AB

and

AC

of this triangle and intersects the side

BC

at the points

K

and

L

. The segment

AK

intersects the circle

\omega

at a point

M

(apart from

K

). Let

P

and

Q

be the reflections of the point

K

in the points

B

and

C

, respectively. Show that the circumcircle of triangle

PMQ

is tangent to the circle

\omega

Problem Statement