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Equilateral triangle and an interior point. Seems classical.

Source: 1st Romanian Master in Mathematics (RMIM) 2008, Bucharest, Problem 1

February 9, 2008
conicsgeometry unsolvedgeometry

Problem Statement

Let ABC ABC be an equilateral triangle and P P in its interior. The distances from P P to the triangle's sides are denoted by a2,b2,c2 a^2, b^2,c^2 respectively, where a,b,c>0 a,b,c>0. Find the locus of the points P P for which a,b,c a,b,c can be the sides of a non-degenerate triangle.
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