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Junior Balkan MO
2012 Junior Balkan MO
2
2
Part of
2012 Junior Balkan MO
Problems
(1)
JBMO 2012 Problem 2
Source: JBMO 2012
6/27/2012
Let the circles
k
1
k_1
k
1
and
k
2
k_2
k
2
intersect at two points
A
A
A
and
B
B
B
, and let
t
t
t
be a common tangent of
k
1
k_1
k
1
and
k
2
k_2
k
2
that touches
k
1
k_1
k
1
and
k
2
k_2
k
2
at
M
M
M
and
N
N
N
respectively. If
t
⊥
A
M
t\perp AM
t
⊥
A
M
and
M
N
=
2
A
M
MN=2AM
MN
=
2
A
M
, evaluate the angle
N
M
B
NMB
NMB
.
geometry
JBMO