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National and Regional Contests
Azerbaijan Contests
Azerbaijan Junior National Olympiad
2016 Azerbaijan Junior Mathematical Olympiad
4
easy geometry
easy geometry
Source:
February 7, 2016
geometry
circumcircle
Problem Statement
Let
O
O
O
be the circumcenter of
△
A
B
C
.
\triangle ABC.
△
A
BC
.
The circle
k
k
k
passing through
A
A
A
and
B
B
B
cuts
A
C
AC
A
C
and
B
C
BC
BC
at
P
P
P
and
Q
,
Q,
Q
,
respectively. Prove that
P
Q
PQ
PQ
and
O
C
OC
OC
are perpendicular.
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