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<ABP=<ACP if BAP=<CAQ and PBQC parallelogram

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2013 Shortlist G2 day1

September 26, 2021
parallelogramequal anglesgeometry

Problem Statement

Consider the triangle ABCABC. Let P,QP, Q inside the angle AA such that ∠BAP=∠CAQ\angle BAP=\angle CAQ and PBQCPBQC is a parallelogram. Show that ∠ABP=∠ACP.\angle ABP=\angle ACP.
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