An Incenter Combination

★ 7/10plane geometry Triangle Geometry vectors

Problem

Let $I$ be the incenter of $\triangle ABC$ with $AB = 2$ and $AC = 3$ , and write

\overrightarrow{AI} = x\overrightarrow{AB} + y\overrightarrow{AC}, \qquad m = 2x + 3y.

Find the range of possible values of $m$ as the triangle varies.

Answer

Solution

Difficulty	7/10
Topics	plane geometry, Triangle Geometry, vectors

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