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2019 IGO Intermediate P5

Source: 6th Iranian Geometry Olympiad (Intermediate) P5

September 20, 2019

IGOIrangeometry

Problem Statement

Let

ABC

be a triangle with

\angle A = 60^\circ

. Points

E

and

F

are the foot of angle bisectors of vertices

B

and

C

respectively. Points

P

and

Q

are considered such that quadrilaterals

AB

and

CEQF

are parallelograms. Prove that

\angle PAQ > 150^\circ

. (Consider the angle

PAQ

that does not contain side

AB

of the triangle.)
Proposed by Alireza Dadgarnia

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