MathDB
Congruent inscribed circles

Source: IMO LongList 1988, USA 2, Problem 82 of ILL

November 9, 2005
geometryinradiusPythagorean Theoremgeometry unsolved

Problem Statement

The triangle ABCABC has a right angle at C.C. The point PP is located on segment ACAC such that triangles PBAPBA and PBCPBC have congruent inscribed circles. Express the length x=PCx = PC in terms of a=BC,b=CAa = BC, b = CA and c=AB.c = AB.
Back to ProblemsView on AoPS