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National and Regional Contests
China Contests
China Northern MO
2019 China Northern MO
5
2019 CNMO P5
2019 CNMO P5
Source: 2019 China North MO, Problem 5
February 22, 2020
geometry
Problem Statement
Two circles
O
1
O_1
O
1
and
O
2
O_2
O
2
intersect at
A
,
B
A,B
A
,
B
. Bisector of outer angle
∠
O
1
A
O
2
\angle O_1AO_2
∠
O
1
A
O
2
intersects
O
1
O_1
O
1
at
C
C
C
,
O
2
O_2
O
2
at
D
D
D
.
P
P
P
is a point on
⊙
(
B
C
D
)
\odot(BCD)
⊙
(
BC
D
)
,
C
P
∩
O
1
=
E
,
D
P
∩
O
2
=
F
CP\cap O_1=E,DP\cap O_2=F
CP
∩
O
1
=
E
,
D
P
∩
O
2
=
F
. Prove that
P
E
=
P
F
PE=PF
PE
=
PF
.
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