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Some geometry

Source: St Petersburg Olympiad 2012, Grade 9, P6

September 29, 2017
geometry

Problem Statement

ABCABC is triangle. Point LL is inside ABCABC and lies on bisector of ∠B\angle B. KK is on BLBL. ∠KAB=∠LCB=α\angle KAB=\angle LCB= \alpha. Point PP inside triangle is such, that AP=PCAP=PC and ∠APC=2∠AKL\angle APC=2\angle AKL. Prove that ∠KPL=2α\angle KPL=2\alpha
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