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Sum of segments of inscribed n-gon vertices and circle point

Source: IMO Longlist 1989, Problem 58

September 18, 2008
complex numbersgeometry unsolvedgeometry

Problem Statement

A regular n\minus{}gon A1A2A3⋯Ak⋯An A_1A_2A_3 \cdots A_k \cdots A_n inscribed in a circle of radius R R is given. If S S is a point on the circle, calculate T \equal{} \sum^n_{k\equal{}1} SA^2_k.
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