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computational without circles (2006 HOMC Junior Q8)

Source:

July 18, 2019
geometryparallel

Problem Statement

In △ABC,PQ//BC\vartriangle ABC, PQ // BC where PP and QQ are points on ABAB and ACAC respectively. The lines PCPC and QBQB intersect at GG. It is also given EF//BCEF//BC, where G∈EF,E∈ABG \in EF, E \in AB and F∈ACF\in AC with PQ=aPQ = a and EF=bEF = b. Find value of BCBC.
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