Minh Ha Nyugen and Nikolaos Dergiades, Garfunkel's Inequality,
Forum Geometricorum, 4 (2004) 153--156.

Abstract: Let I be the incenter of triangle ABC and U, V, W the intersections of the segments IA, IB, IC with the incircle. If the centroid G is inside the incircle, and D, E, F the intersections of the segments GA, GB, GC with the incircle. Jack Garfunkel [Crux Mathematicorum, Problem 648] asked for a proof that the perimeter of UVW is not greater than that of DEF. This problem is hitherto unsolved. We give a proof in this note.

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