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