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ratio chasing inside a triangle, double segment

Source: CRMO 2012 Region 4 p5

September 30, 2018
ratiogeometrymidpoint

Problem Statement

Let ABCABC be a triangle. Let EE be a point on the segment BCBC such that BE=2ECBE = 2EC. Let FF be the mid-point of ACAC. Let BFBF intersect AEAE in QQ. Determine BQ:QFBQ:QF.
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