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Two circumcircles are tangent

Source: ITAMO 2021 - Problem 2

May 8, 2021

geometrycircumcircle

Problem Statement

Let

ABC

a triangle and let

I

be the center of its inscribed circle. Let

D

be the symmetric point of

I

with respect to

AB

and

E

be the symmetric point of

I

with respect to

AC

. Show that the circumcircles of the triangles

BID

and

CIE

are eachother tangent.

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