CMO 1971 Problem 8
- Paper
A regular pentagon is inscribed in a circle of radius . is any point inside the pentagon. Perpendiculars are dropped from to the sides, or the sides produced, of the pentagon.
a) Prove that the sum of the lengths of these perpendiculars is constant. b) Express this constant in terms of the radius .
Dataset text AI-MO AoPS. Quoted with source.
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