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Caucasus Mathematical Olympiad
2019 Caucasus Mathematical Olympiad
2
2
Part of
2019 Caucasus Mathematical Olympiad
Problems
(1)
Two circles intersect on circumcircle
Source: IV Caucasus Mathematic Olympiad
4/7/2019
In a triangle
A
B
C
ABC
A
BC
let
I
I
I
be the incenter. Prove that the circle passing through
A
A
A
and touching
B
I
BI
B
I
at
I
I
I
, and the circle passing through
B
B
B
and touching
A
I
AI
A
I
at
I
I
I
, intersect at a point on the circumcircle of
A
B
C
ABC
A
BC
.
geometry
circumcircle