MathDB

Two circles

\omega_1

and

\omega_2

intersecting at points

X{}

and

Y{}

are inside the circle

\Omega

and touch it at points

A{}

and

B{}

, respectively; the segments

AB

and

XY

intersect. The line

AB

intersects the circles

\omega_1

and

\omega_2

again at points

C{}

and

D{}

, respectively. The circle inscribed in the curved triangle

CDX

touches the side

CD

at the point

Z{}

. Prove that

XZ

is a bisector of

\angle AXB{}

Problem Statement