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Auxiliary Lines in a Triangle

Source: Indian RMO 2013 Mumbai Region Problem 4

February 1, 2014
ratiogeometry unsolvedgeometry

Problem Statement

In a triangle ABCABC, points DD and EE are on segments BCBC and ACAC such that BD=3DCBD=3DC and AE=4ECAE=4EC. Point PP is on line EDED such that DD is the midpoint of segment EPEP. Lines APAP and BCBC intersect at point SS. Find the ratio BS/SDBS/SD.
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