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Hard geometry

Source: China South East Mathematical Olympiad 2016 Grade 10 Prob.2

July 30, 2016
geometry

Problem Statement

Suppose PABPAB and PCDPCD are two secants of circle OO. Lines AD∩BC=QAD \cap BC=Q. Point TT lie on segment BQBQ and point KK is intersection of segment PTPT with circle OO, S=QK∩PAS=QK\cap PA Given that ST∥PQST \parallel PQ, prove that B,S,K,TB,S,K,T lie on a circle.
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