MathDB
Problem 5

Source: Paraguayan Mathematical Olympiad 2012

October 15, 2012
geometrycircumcircletrigonometrygeometry proposed

Problem Statement

Let ABCABC be an equilateral triangle. Let QQ be a random point on BCBC, and let PP be the meeting point of AQAQ and the circumscribed circle of △ABC\triangle ABC. Prove that 1PQ=1PB+1PC\frac{1}{PQ}=\frac{1}{PB}+\frac{1}{PC}.
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