The incenter of a triangle is the point of concurrency of the angle bisectors. Does a rectangle have an incenter?

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  if and only if the rectangle is a square

Step-by-step explanation:

The angle bisectors of a rectangle will meet at a single point if, and only if, the rectangle is a square.

In general, a rectangle does not have an incenter.

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The incircle must be tangent to all sides of the polygon. That cannot be the case unless the rectangle has its length equal to its width. That is, it must be a square.

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