A Tetrahedron Dot Constraint

★ 8/10Substitution solid geometry AM-GM vectors

Problem

In a tetrahedron $D\text{-}ABC$ , $AB = 2$ and $\overrightarrow{AC}\cdot\overrightarrow{BD} = -3$ . With $AD = a$ , $BC = b$ , $CD = c$ , find the minimum value of

\frac{c^2}{ab + 1}.

Answer

Solution

Difficulty	8/10
Topics	Substitution, solid geometry, AM-GM, vectors

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