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angle chasing, double angle given, perpendicularity wanted

Source: Ukrainian Geometry Olympiad 2017 XI p2

December 12, 2018
geometryAngle Chasingperpendicularity

Problem Statement

On the side ACAC of a triangle ABCABC, let a KK be a point such that AK=2KCAK = 2KC and ∠ABK=2∠KBC\angle ABK = 2 \angle KBC. Let FF be the midpoint of ACAC, LL be the projection of AA on BKBK. Prove that FL⊥BCFL \bot BC.
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