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Inequality on altitudes - [Iran Second Round 1988]

Source:

December 7, 2010
inequalitiesgeometry3D geometrytetrahedronPythagorean Theoremgeometry proposed

Problem Statement

In tetrahedron ABCDABCD let ha,hb,hch_a, h_b, h_c and hdh_d be the lengths of the altitudes from each vertex to the opposite side of that vertex. Prove that 1ha<1hb+1hc+1hd.\frac{1}{h_a} <\frac{1}{h_b}+\frac{1}{h_c}+\frac{1}{h_d}.
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