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Problems
Contests
National and Regional Contests
Turkey Contests
Turkey EGMO TST
2015 Turkey EGMO TST
2
2
Part of
2015 Turkey EGMO TST
Problems
(1)
Point Inside Triangle
Source: Turkey EGMO TST 2015 P2
8/7/2016
Let
D
D
D
be the midpoint of the side
B
C
BC
BC
of a triangle
A
B
C
ABC
A
BC
and
P
P
P
be a point inside the
A
B
D
ABD
A
B
D
satisfying
∠
P
A
D
=
9
0
∘
−
∠
P
B
D
=
∠
C
A
D
\angle PAD=90^\circ - \angle PBD=\angle CAD
∠
P
A
D
=
9
0
∘
−
∠
PB
D
=
∠
C
A
D
. Prove that
∠
P
Q
B
=
∠
B
A
C
\angle PQB=\angle BAC
∠
PQB
=
∠
B
A
C
, where
Q
Q
Q
is the intersection point of the lines
P
C
PC
PC
and
A
D
AD
A
D
.
geometry