The incenter of a triangle is the center of which circle?

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Multiple Choice

The incenter of a triangle is the center of which circle?

The incenter is the point where the angle bisectors meet, and it is equidistant from all three sides of the triangle. The circle centered at that point with a radius equal to that common distance is tangent to each side, fitting inside the triangle. This circle is called the incircle, so the incenter is the center of the incircle. The other circles have different roles: a circumcircle passes through the triangle’s vertices; a nine-point circle relates to the midpoints and feet of the altitudes; an excircle is tangent to the extensions of the sides outside the triangle.

The incenter is the point where the angle bisectors meet, and it is equidistant from all three sides of the triangle. The circle centered at that point with a radius equal to that common distance is tangent to each side, fitting inside the triangle. This circle is called the incircle, so the incenter is the center of the incircle.

The other circles have different roles: a circumcircle passes through the triangle’s vertices; a nine-point circle relates to the midpoints and feet of the altitudes; an excircle is tangent to the extensions of the sides outside the triangle.

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