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points on semicircles, max sum of triangle areas

Source: Polish MO Finals 1970 p1

August 22, 2024
geometryGeometric Inequalities

Problem Statement

Diameter ABAB divides a circle into two semicircles. Points P1P_1 , P2P_2, ......, PnP_n are given on one of the semicircles in this order. How should a point C be chosen on the other semicircle in order to maximize the sum of the areas of triangles CP1P2CP_1P_2, CP2P3CP_2P_3, ......,CPn−1PnCP_{n-1}P_n?
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