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1999 Korea Junior Math Olympiad
5
Easy circumcircle problem KJMO 1999 P5
Easy circumcircle problem KJMO 1999 P5
Source: 1999 KJMO P5
June 30, 2024
geometry
circumcircle
KJMO
Problem Statement
O
O
O
is a circumcircle of
A
B
C
ABC
A
BC
and
C
O
CO
CO
meets
A
B
AB
A
B
at
P
P
P
, and
B
O
BO
BO
meets
A
C
AC
A
C
at
Q
Q
Q
. Show that
B
P
=
P
Q
=
Q
C
BP=PQ=QC
BP
=
PQ
=
QC
if and only if
∠
A
=
6
0
∘
\angle A=60^{\circ}
∠
A
=
6
0
∘
.
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