Problem

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Tags: geometry, trapezoid, trigonometry, incenter, modular arithmetic, ratio, parallelogram



We are given an isosceles triangle ABC such that BC=a and AB=BC=b. The variable points M(AC) and N(AB) satisfy a2AMAN=b2BNCM. The straight lines BM and CN intersect in P. Find the locus of the variable point P. Dan Branzei