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an excircle and 4 points

Source: Saint Petersburg MO 2020 Grade 9 Problem 5

May 7, 2020

geometrycircumcircleinradius

Problem Statement

Point

I_a

is the

A

-excircle center of

I_aX, BA'

which is tangent to

BC

at

X

. Let

A'

be diametrically opposite point of

A

with respect to the circumcircle of

\triangle ABC

. On the segments

I_aX, BA'

and

CA'

are chosen respectively points

Y,Z

and

T

such that

I_aY=BZ=CT=r

where

r

is the inradius of

\triangle ABC

. Prove that the points

X,Y,Z

and

T

are concyclic.

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