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easy geometry

Source: Iran team selection test third exam p1

June 4, 2015
geometryradical axis

Problem Statement

Point AA is outside of a given circle ω\omega. Let the tangents from AA to ω\omega meet ω\omega at S,TS, T points X,YX, Y are midpoints of AT,ASAT, AS let the tangent from XX to ω\omega meet ω\omega at R≠TR\neq T. points P,QP, Q are midpoints of XT,XRXT, XR let XY∩PQ=K,SX∩TK=LXY\cap PQ=K, SX\cap TK=L prove that quadrilateral KRLQKRLQ is cyclic.
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