The Circumcenter and a Product

★ 7/10plane geometry Law of Sines trigonometry Extrema Law of Cosines vectors

Problem

Let $O$ be the circumcenter of $\triangle ABC$ , with $|AB| = 2$ and $|AC| = 4$ . Find the minimum value of

|AO| \cdot |BC|.

Answer

Solution

Difficulty	7/10
Topics	plane geometry, Law of Sines, trigonometry, Extrema, Law of Cosines, vectors

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