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Italy Contests
ITAMO
2021 ITAMO
2
2
Part of
2021 ITAMO
Problems
(1)
Two circumcircles are tangent
Source: ITAMO 2021 - Problem 2
5/8/2021
Let
A
B
C
ABC
A
BC
a triangle and let
I
I
I
be the center of its inscribed circle. Let
D
D
D
be the symmetric point of
I
I
I
with respect to
A
B
AB
A
B
and
E
E
E
be the symmetric point of
I
I
I
with respect to
A
C
AC
A
C
. Show that the circumcircles of the triangles
B
I
D
BID
B
I
D
and
C
I
E
CIE
C
I
E
are eachother tangent.
geometry
circumcircle