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intersecting circles given, segment parallel to given tangent wanted

Source: ITAMO 1986 p1

February 2, 2020
parallelcirclestangentgeometry

Problem Statement

Two circles α\alpha and β\beta intersect at points PP and QQ. The lines connecting a point RR on β\beta with PP and QQ intersect α\alpha again at SS and TT respectively. Prove that STST is parallel to the line tangent to β\beta at RR.
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