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• Given a triangle ABC, how would you use only a compass and straight edge to find a point P such that triangles ABP, ACP and BCP have equal perimeters?  (Assume that ABC is constructed so that a solution does exist.)

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1. Submitted By: arun — July 30, 2007 -1 votes   + -

   If it is a equilateral triangle, create a point p in the centre of the equilateral triangle by using the compass.

   For all the other triangles, create a mirror of the existing triangle using its longest section as one side of the mirrored triangle.

   Use compass to get the length of the other sides using the two points AB, BC, AC from the existing triangle. Make arc using the lengths to create the point p. Use the straight edge to connect point p to A, B and C.

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