MathDB

AT passes through an intersection of (J) and (DEF ), incenter, excenter

Source: 2021 Saudi Arabia Training Lists p12 https://artofproblemsolving.com/community/c2758131_2021_saudi_arabia_training_tests

January 5, 2022

geometryincenterexcentercollinear

Problem Statement

Let

ABC

be a triangle with circumcenter

O

and incenter

I

, ex-center in angle

A

J

. Denote

D

as the tangent point of

(I)

BC

and the angle bisector of angle

A

cuts

BC

(O)

respectively at

E, F

. The circle

(DEF )

meets

(O)

again at

T

. Prove that

AT

passes through an intersection of

(J)

and

(DEF )