MathDB

Given a triangle

ABC

with circumcircle

\Gamma

. Points

E

and

F

are the foot of angle bisectors of

B

and

C

I

is incenter and

K

is the intersection of

AI

and

EF

. Suppose that

T

be the midpoint of arc

BAC

. Circle

\Gamma

intersects the

A

-median and circumcircle of

AEF

for the second time at

X

and

S

. Let

S'

be the reflection of

S

across

AI

and

J

be the second intersection of circumcircle of

AS'K

and

AX

. Prove that quadrilateral

TJIX

is cyclic.
Proposed by Alireza Dadgarnia and Amir Parsa Hosseini

Problem Statement