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D >= 2d, max and min distance of a point from perimeter of acute triangle

Source: Eotvos 1943 p2

September 10, 2024
geometryperimetergeometric inequality

Problem Statement

Let PP be any point inside an acute triangle. Let DD and dd be respectively the maximum and minimum distances from PP to any point on the perimeter of the triangle. (a) Prove that D≥2dD \ge 2d. (b) Determine when equality holds
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