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Median has fixed length

Source: Iranian National Olympiad (3rd Round) 2003

January 24, 2009
vectortrigonometrygeometrytrapezoidabsolute valuetrig identitiesLaw of Cosines

Problem Statement

Circles C1,C2 C_1,C_2 intersect at P P. A line Δ \Delta is drawn arbitrarily from P P and intersects with C1,C2 C_1,C_2 at B,C B,C. What is locus of A A such that the median of AM AM of triangle ABC ABC has fixed length k k.
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