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Germany Contests
Germany Team Selection Test
2012 Germany Team Selection Test
2
2
Part of
2012 Germany Team Selection Test
Problems
(1)
The Wrong Problem
Source: Germany TST 2012 P2
4/13/2020
Let
Γ
\Gamma
Γ
be the circumcircle of isosceles triangle
A
B
C
ABC
A
BC
with vertex
C
C
C
. An arbitrary point
M
M
M
is chosen on the segment
B
C
BC
BC
and point
N
N
N
lies on the ray
A
M
AM
A
M
with
M
M
M
between
A
,
N
A,N
A
,
N
such that
A
N
=
A
C
AN=AC
A
N
=
A
C
. The circumcircle of
C
M
N
CMN
CMN
cuts
Γ
\Gamma
Γ
in
P
P
P
other than
C
C
C
and
A
B
,
C
P
AB,CP
A
B
,
CP
intersect at
Q
Q
Q
. Prove that
∠
B
M
Q
=
∠
Q
M
N
.
\angle BMQ = \angle QMN.
∠
BMQ
=
∠
QMN
.
geometry
circumcircle