MathDB

The point

K{}

is the middle of the arc

BAC

of the circumcircle of the triangle

ABC

. The point

I{}

is the center of its inscribed circle

\omega

. The line

KI

intersects the circumcircle of the triangle

ABC

T{}

for the second time. Prove that the circle passing through the midpoints of the segments

BC, BT

and

CT

is tangent to the circle which is symmetric to

\omega

with respect to

BC

Problem Statement