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a^2.AM.AN=b^2.BN.CM

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August 18, 2010
geometrytrapezoidtrigonometryincentermodular arithmeticratioparallelogram

Problem Statement

We are given an isosceles triangle ABCABC such that BC=aBC=a and AB=BC=bAB=BC=b. The variable points M∈(AC)M\in (AC) and N∈(AB)N\in (AB) satisfy a2⋅AM⋅AN=b2⋅BN⋅CMa^2\cdot AM \cdot AN = b^2 \cdot BN \cdot CM. The straight lines BMBM and CNCN intersect in PP. Find the locus of the variable point PP.
Dan Branzei
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