A Centroid Right-Angle Relation

★ 8/10plane geometry trigonometry Law of Cosines Triangle Geometry vectors

Problem

Let $G$ be the centroid of $\triangle ABC$ with $AG\perp BG$ , and

\frac 1{\tan A}+\frac 1{\tan B}=\frac{\lambda}{\tan C}.

Find $\lambda$ .

Answer

Solution

Difficulty	8/10
Topics	plane geometry, trigonometry, Law of Cosines, Triangle Geometry, vectors

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