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International Contests
Caucasus Mathematical Olympiad
2022 Caucasus Mathematical Olympiad
6
6
Part of
2022 Caucasus Mathematical Olympiad
Problems
(1)
Find the angle
Source: VII Caucasus Olympiad, Senior, Day2 P6
3/13/2022
Let
A
B
C
ABC
A
BC
be an acute triangle. Let
P
P
P
be a point on the circle
(
A
B
C
)
(ABC)
(
A
BC
)
, and
Q
Q
Q
be a point on the segment
A
C
AC
A
C
such that
A
P
⊥
B
C
AP\perp BC
A
P
⊥
BC
and
B
Q
⊥
A
C
BQ\perp AC
BQ
⊥
A
C
. Lot
O
O
O
be the circumcenter of triangle
A
P
Q
APQ
A
PQ
. Find the angle
O
B
C
OBC
OBC
.
geometry
circumcircle