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Geometry in 2019 China Second Round(B)

Source: 2019 China Second Round(B) P3

September 8, 2019
geometry

Problem Statement

Point A,B,C,D,EA,B,C,D,E lie on a line in this order, such that BC=CD=AB⋅DE,BC=CD=\sqrt{AB\cdot DE}, PP doesn't lie on the line, and satisfys that PB=PD.PB=PD. Point K,LK,L lie on the segment PB,PD,PB,PD, respectively, such that KCKC bisects ∠BKE,\angle BKE, and LCLC bisects ∠ALD.\angle ALD. Prove that A,K,L,EA,K,L,E are concyclic.
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