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Sharygin Geometry Olympiad
2021 Sharygin Geometry Olympiad
9.5
9.5
Part of
2021 Sharygin Geometry Olympiad
Problems
(1)
circumcircle of AXY passes through circumceuters of AOB and AOC
Source: 2021 Sharygin Geometry Olympiad Finals grade IX p5
8/2/2021
Let
O
O
O
be the clrcumcenter of triangle
A
B
C
ABC
A
BC
. Points
X
X
X
and
Y
Y
Y
on side
B
C
BC
BC
are such that
A
X
=
B
X
AX = BX
A
X
=
BX
and
A
Y
=
C
Y
AY = CY
A
Y
=
C
Y
. Prove that the circumcircle of triangle
A
X
Y
AXY
A
X
Y
passes through the circumceuters of triangles
A
O
B
AOB
A
OB
and
A
O
C
AOC
A
OC
.
Concyclic
Circumcenter
geometry