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1988 USAMO
4
4
Part of
1988 USAMO
Problems
(1)
1988 USAMO Problem 4
Source:
7/27/2011
Let
I
I
I
be the incenter of triangle
A
B
C
ABC
A
BC
, and let
A
′
A'
A
′
,
B
′
B'
B
′
, and
C
′
C'
C
′
be the circumcenters of triangles
I
B
C
IBC
I
BC
,
I
C
A
ICA
I
C
A
, and
I
A
B
IAB
I
A
B
, respectively. Prove that the circumcircles of triangles
A
B
C
ABC
A
BC
and
A
′
B
′
C
′
A'B'C'
A
′
B
′
C
′
are concentric.
AMC
USA(J)MO
USAMO
geometry
incenter
circumcircle