MathDB

2016 ISL G2 vibes?

Source: Serbia MO 2023 P6

April 2, 2023

geometrymixtilinear incircle

Problem Statement

Given is a triangle

ABC

with incenter

I

and circumcircle

\omega

. The incircle is tangent to

BC

at

D

. The perpendicular at

I

to

AI

meets

AB, AC

at

E, F

and the circle

(AEF)

meets

\omega

and

\omega

at

G, H

. The tangent at

G

to

\omega

meets

BC

at

J

and

AJ

meets

\omega

at

K

. Prove that

(DJK)

and

(GIH)

are tangent to each other.

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