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2021 Ukraine National Mathematical Olympiad
8.4
Two points inside isosceles triangle
Two points inside isosceles triangle
Source: Ukraine MO 2021 8.4
May 2, 2021
geometry
Problem Statement
Let
A
B
C
ABC
A
BC
be an isosceles triangle with
A
B
=
A
C
AB = AC
A
B
=
A
C
. Points
P
P
P
and
Q
Q
Q
inside
△
A
B
C
\triangle ABC
△
A
BC
are such that
∠
B
P
C
=
3
2
∠
B
A
C
\angle BPC = \frac{3}{2} \angle BAC
∠
BPC
=
2
3
∠
B
A
C
,
B
P
=
A
Q
BP = AQ
BP
=
A
Q
and
A
P
=
C
Q
AP = CQ
A
P
=
CQ
. Prove that
A
P
=
P
Q
AP = PQ
A
P
=
PQ
.Proposed by Fedir Yudin
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