MathDB

Let

I

be the incenter of triangle

ABC

, and let

\omega

be its incircle. Let

E

and

F

be the points of tangency of

\omega

with

CA

and

AB

, respectively. Let

X

and

Y

be the intersections of the circumcircle of

BIC

and

\omega

. Take a point

T

BC

such that

\angle AIT

is a right angle. Let

G

be the intersection of

EF

and

BC

, and let

Z

be the intersection of

XY

and

AT

. Prove that

AZ

ZG

, and

AI

form an isosceles triangle.
Proposed by Li4 and usjl.

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