Range of a Coefficient Sum on a Circular Arc

★ 6/10plane geometry Extrema AM-GM vectors

Problem

In sector $AOB$ the central angle is $120^\circ$ . $P$ is a point on arc $AB$ , and $\overrightarrow{OP} = x\,\overrightarrow{OA} + y\,\overrightarrow{OB}$ . Find the range of $x + y$ .

Answer

Solution

Difficulty	6/10
Topics	plane geometry, Extrema, AM-GM, vectors

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