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Contests
National and Regional Contests
Lithuania Contests
Grand Duchy of Lithuania
2014 Grand Duchy of Lithuania
2
2
Part of
2014 Grand Duchy of Lithuania
Problems
(1)
Prove that APM + BPC = 180
Source: 6th Grand Duchy of Lithuania contest
12/31/2014
An isosceles triangle
A
B
C
ABC
A
BC
with
A
C
=
B
C
AC = BC
A
C
=
BC
is given. Let
M
M
M
be the midpoint of the side
A
B
AB
A
B
and let
P
P
P
be a point inside the triangle such that
∠
P
A
B
=
∠
P
B
C
\angle PAB = \angle PBC
∠
P
A
B
=
∠
PBC
. Prove that \angle APM + \angle BPC = 180 \textdegree
geometry
circumcircle
geometry proposed