Maximum Cosine in a Tetrahedron

★ 7/10Extrema solid geometry Symmetry vectors

Problem

In the tetrahedron $P\text{-}ABC$ shown in the figure,

AB = AC = PB = PC = 10, \quad PA = 8, \quad BC = 12.

A point $M$ lies in the plane $PBC$ and satisfies $AM = 7$ . Let $\alpha$ be the angle between the lines $AM$ and $BC$ . Find the maximum value of $\cos \alpha$ .

Answer

Solution

Difficulty	7/10
Topics	Extrema, solid geometry, Symmetry, vectors

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