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H >=r+R where H is max altitude

Source: 1978 Hungary - Kürschák Competition p3

October 15, 2022
geometryGeometric Inequalitiesinequalities

Problem Statement

A triangle has inradius rr and circumradius RR. Its longest altitude has length HH. Show that if the triangle does not have an obtuse angle, then H≥r+RH \ge r+R. When does equality hold?
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