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Angle chasings

Source: 2020 Tuymaada Junior P6

October 6, 2020
geometry

Problem Statement

AKAK and BLBL are altitudes of an acute triangle ABCABC. Point PP is chosen on the segment AKAK so that LK=LPLK=LP. The parallel to BCBC through PP meets the parallel to PLPL through BB at point QQ. Prove that ∠AQB=∠ACB\angle AQB = \angle ACB.
(S. Berlov)
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