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2007 JBMO Shortlist G3

Source: 2007 JBMO Shortlist G3

October 10, 2017
geometryJBMO

Problem Statement

Let the inscribed circle of the triangle △ABC\vartriangle ABC touch side BCBC at MM , side CACA at NN and side ABAB at PP . Let DD be a point from [NP]\left[ NP \right] such that DPDN=BDCD\frac{DP}{DN}=\frac{BD}{CD} . Show that DM⊥PNDM \perp PN .
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