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ratio chasing inside a triangle, segment trisecting

Source: CRMO 2012 Region 2 p5

September 30, 2018
ratiogeometrymidpoint

Problem Statement

Let ABCABC be a triangle. Let D,ED, E be a points on the segment BCBC such that BD=DE=ECBD =DE = EC. Let FF be the mid-point of ACAC. Let BFBF intersect ADAD in PP and AEAE in QQ respectively. Determine BP:PQBP:PQ.
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