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Caracterizing right-angled triangles

Source: Problem 6 - Brazil Math Olympiad 1994

March 17, 2006
geometryperimetercircumcircleinradiusgeometry proposed

Problem Statement

A triangle has semi-perimeter ss, circumradius RR and inradius rr. Show that it is right-angled iff 2R=sāˆ’r2R = s - r.
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