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PJ // AC iff BC^2 = AC· QC

Source: Mexican Mathematical Olympiad 1998 OMM P5

July 28, 2018
geometryTangents

Problem Statement

The tangents at points BB and CC on a given circle meet at point AA. Let QQ be a point on segment ACAC and let BQBQ meet the circle again at PP. The line through QQ parallel to ABAB intersects BCBC at JJ. Prove that PJPJ is parallel to ACAC if and only if BC2=ACā‹…QCBC^2 = AC\cdot QC.
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