MathDB

Let

AA'BCC'B'

be a convex cyclic hexagon such that

AC

is tangent to the incircle of the triangle

A'B'C'

, and

A'C'

is tangent to the incircle of the triangle

ABC

. Let the lines

AB

and

A'B'

meet at

X

and let the lines

BC

and

B'C'

meet at

Y

.
Prove that if

XBYB'

is a convex quadrilateral, then it has an incircle.

Problem Statement