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Sharygin Geometry Olympiad
2022 Sharygin Geometry Olympiad
2
2
Part of
2022 Sharygin Geometry Olympiad
Problems
(1)
Circumcenter lies on bisector ...
Source: Sharygin GO - 2022 - P2 (grade-8)
3/4/2022
Let
A
B
C
D
ABCD
A
BC
D
be a curcumscribed quadrilateral with incenter
I
I
I
, and let
O
1
,
O
2
O_{1}, O_{2}
O
1
,
O
2
be the circumcenters of triangles
A
I
D
AID
A
I
D
and
C
I
D
CID
C
I
D
. Prove that the circumcenter of triangle
O
1
I
O
2
O_{1}IO_{2}
O
1
I
O
2
lies on the bisector of angle
A
B
C
ABC
A
BC
geometry
circumcircle