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distances of a center in circle from sides of isosceles triangle

Source: 2006 Spanish Mathematical Olympiad P3

July 20, 2018
geometrycircumcircledistanceisosceles

Problem Statement

ABCABC is an isosceles triangle with AB=ACAB = AC. Let PP be any point of a circle tangent to the sides ABAB in BB and to AC in C. Denote aa, bb and cc to the distances from PP to the sides BC,ACBC, AC and ABAB respectively. Prove that: a2=bca^2=bc
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