A Cevian of Length One

★ 7/10trigonometry Law of Cosines Monotonicity inequality Triangle Geometry vectors

Problem

In $\triangle ABC$ , $B = \dfrac{2\pi}{3}$ and $BC > AB$ . A point $D$ satisfies $\overrightarrow{AD} = 2\overrightarrow{DC}$ and $BD = 1$ . Find the range of possible values of $AC$ .

Answer

Solution

Difficulty	7/10
Topics	trigonometry, Law of Cosines, Monotonicity, inequality, Triangle Geometry, vectors

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