MathDB

Incircle

\omega

of triangle

ABC

is tangent to sides

CB

and

CA

D

and

E

, respectively. Point

X

is the reflection of

D

with respect to

B

. Suppose that the line

DE

is tangent to the

A

-excircle at

Z

. Let the circumcircle of triangle

XZE

intersect

\omega

for the second time at

K

. Prove that the intersection of

BK

and

AZ

lies on

\omega

.
Proposed by Mahdi Etesamifard and Alireza Dadgarnia

Problem Statement