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inradius r=1/2 (a + b - c) in right triangle (2016 Izumrud Olympiad 8-9 p5)

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May 4, 2021
geometryinradiusright triangle

Problem Statement

Prove that if aa and bb are legs, cc is the hypotenuse of a right triangle, then the radius of a circle inscribed in this triangle can be found by the formula r=12(a+bc)r = \frac12 (a + b - c).