A Circumcenter Identity

★ 7/10Law of Sines trigonometry Trigonometric Identities vectors

Problem

Let $O$ be the circumcenter of $\triangle ABC$ with $A = \dfrac{\pi}{3}$ , and suppose

\frac{\cos B}{\sin C}\overrightarrow{AB} + \frac{\cos C}{\sin B}\overrightarrow{AC} = 2m\overrightarrow{AO}.

Find $m$ .

Answer

Solution

Difficulty	7/10
Topics	Law of Sines, trigonometry, Trigonometric Identities, vectors

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