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Quadrilateral and incircles

Source: Russian TST 2022, Day 7 P2

March 21, 2023

geometryConcyclicincircle

Problem Statement

The quadrilateral

ABCD

is inscribed in the circle

\Gamma

. Let

I_B

and

I_D

be the centers of the circles

\omega_B

and

\omega_D

inscribed in the triangles

ABC

and

ADC

, respectively. A common external tangent to

\omega_B

and

\omega_D

intersects

\Gamma

at

K

and

L{}

. Prove that

I_B,I_D,K

and

L{}

lie on the same circle.

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