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2004 JBMO Shortlist
1
1
Part of
2004 JBMO Shortlist
Problems
(1)
3 circles, 1 centered in the intersection of the 2 others
Source: JBMO Shortlist 2004
10/13/2017
Two circles
C
1
C_1
C
1
and
C
2
C_2
C
2
intersect in points
A
A
A
and
B
B
B
. A circle
C
C
C
with center in
A
A
A
intersect
C
1
C_1
C
1
in
M
M
M
and
P
P
P
and
C
2
C_2
C
2
in
N
N
N
and
Q
Q
Q
so that
N
N
N
and
Q
Q
Q
are located on different sides wrt
M
P
MP
MP
and
A
B
>
A
M
AB> AM
A
B
>
A
M
. Prove that
∠
M
B
Q
=
∠
N
B
P
\angle MBQ = \angle NBP
∠
MBQ
=
∠
NBP
.
JBMO
geometry