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Serbia Team Selection Test
2013 Serbia Additional Team Selection Test
2
Serbia additional TST 2013
Serbia additional TST 2013
Source:
May 22, 2015
geometry
Problem Statement
In an acute
△
A
B
C
\triangle ABC
△
A
BC
(
A
B
≠
A
C
AB \neq AC
A
B
=
A
C
) with angle
α
\alpha
α
at the vertex
A
A
A
, point
E
E
E
is the nine-point center, and
P
P
P
a point on the segment
A
E
AE
A
E
. If
∠
A
B
P
=
∠
A
C
P
=
x
\angle ABP = \angle ACP = x
∠
A
BP
=
∠
A
CP
=
x
, prove that
x
=
90
x = 90
x
=
90
°
−
2
α
-2 \alpha
−
2
α
.Proposed by Dusan Djukic
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