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Perp distances

Source: Indian RMO 2003 Problem 5

October 27, 2005
ratiogeometrysimilar triangles

Problem Statement

Suppose PP is an interior point of a triangle ABCABC such that the ratios d(A,BC)d(P,BC),d(B,CA)d(P,CA),d(C,AB)d(P,AB) \frac{d(A,BC)}{d(P,BC)} , \frac{d(B,CA)}{d(P,CA)} , \frac{d(C,AB)}{d(P,AB)} are all equal. Find the common value of these ratios. d(X,YZ)d(X,YZ) represents the perpendicular distance fro XX to the line YZYZ.
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