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3d geometric inequality

Source: Romanian National Olympiad, grade x, p.1

August 27, 2019
geometry3D geometrytetrahedrongeometric inequalityinequalities

Problem Statement

Let be a tetahedron OABC OABC with OA⊥OB⊥OC⊥OA. OA\perp OB\perp OC\perp OA. Show that OH≤r(1+3), OH\le r\left( 1+\sqrt 3 \right) , where H H is the orthocenter of ABC ABC and r r is radius of the inscribed spere of OABC. OABC.
Valentin Vornicu
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