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4AM=3AC in regular pyramid VABCD

Source: Romanian MO 2010 Grade 8

August 6, 2012
geometry3D geometrypyramidPythagorean Theoremgeometry proposed

Problem Statement

Let VABCDVABCD be a regular pyramid, having the square base ABCDABCD. Suppose that on the line ACAC lies a point MM such that VM=MBVM=MB and (VMB)⊥(VAB)(VMB)\perp (VAB). Prove that 4AM=3AC4AM=3AC.
Mircea Fianu
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