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<BAP =<CAQ wanted, <BAE = <CAF , EP//CD , FQ //CD

Source: 2010 Croatia MO (pre-TST) p3

August 5, 2020

geometryparallelequal angles

Problem Statement

Let

\angle BAE = \angle CAF

be a point on the side

AC

of triangle

ABC

. Let

E

and

F

be points on the segments

BD

and

BC

respectively, such that

\angle BAE = \angle CAF

. Let

P

and

Q

be points on the segments

BC

and

BD

respectively, such that

EP \parallel CD

and

FQ \parallel CD

. Prove that

\angle BAP = \angle CAQ

.

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