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the shortest distance between its incenter and its centroid

Source: Vietnam NMO 1996, problem 5

September 5, 2008
geometryincentergeometry proposed

Problem Statement

The triangle ABC has BC=1 and \angle BAC \equal{} a. Find the shortest distance between its incenter and its centroid. Denote this shortest distance by f(a) f(a). When a varies in the interval (π3,π) (\frac {\pi}{3},\pi), find the maximum value of f(a) f(a).
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