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Japan MO Finals
2009 Japan MO Finals
4
4
Part of
2009 Japan MO Finals
Problems
(1)
If \angle BAO = \angle CAO, then \angle PAO = \angle QAO
Source: 2009 Japan Mathematical Olympiad Finals, Problem 4
2/21/2009
Let
Γ
\Gamma
Γ
be a circumcircle. A circle with center
O
O
O
touches to line segment
B
C
BC
BC
at
P
P
P
and touches the arc
B
C
BC
BC
of
Γ
\Gamma
Γ
which doesn't have
A
A
A
at
Q
Q
Q
. If
∠
B
A
O
=
∠
C
A
O
\angle {BAO} = \angle {CAO}
∠
B
A
O
=
∠
C
A
O
, then prove that
∠
P
A
O
=
∠
Q
A
O
\angle {PAO} = \angle {QAO}
∠
P
A
O
=
∠
Q
A
O
.
geometry
circumcircle