MathDB
Beautiful geometry problem

Source: titu andreescu

October 11, 2005
geometryperimeterconicshyperbolaparallelogramrectangleperpendicular bisector

Problem Statement

Let ABCABC a triangle and PP a point such that the triangles PAB,PBC,PCAPAB, PBC, PCA have the same area and the same perimeter. Prove that if: a) PP is in the interior of the triangle ABCABC then ABCABC is equilateral. b) PP is in the exterior of the triangle ABCABC then ABCABC is right angled triangle.
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