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Interesting tangency Geometry

Source: India EGMO 2022 TST P5

November 28, 2021

geometrygeometry solvedtangent circlesAngle ChasingincenterexcenterInversion

Problem Statement

Let

I

and

I_A

denote the incentre and excentre opposite to

A

of scalene

\triangle ABC

respectively. Let

A'

be the antipode of

A

in

\odot (ABC)

and

L

be the midpoint of arc

(BAC)

. Let

LB

and

LC

intersect

AI

at points

Y

and

Z

respectively. Prove that

\odot (LYZ)

is tangent to

\odot (A'II_A)

.
~Mahavir Gandhi

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