The center of the inscribed circle, equidistant from all sides of a triangle, is called what?

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Multiple Choice

The center of the inscribed circle, equidistant from all sides of a triangle, is called what?

Explanation:
The center of the inscribed circle, equidistant from all sides, is called the incenter. This point sits at the intersection of the triangle’s angle bisectors, and the incircle centered there touches each side, so the distance from the center to any side is the circle’s radius. In other words, the center is chosen so it is the same distance to every side, which defines the incenter. For contrast, the circumcenter is the center of the circle through the vertices (equidistant from the vertices), the centroid is the balance point where the medians meet, and the orthocenter is where the altitudes intersect.

The center of the inscribed circle, equidistant from all sides, is called the incenter. This point sits at the intersection of the triangle’s angle bisectors, and the incircle centered there touches each side, so the distance from the center to any side is the circle’s radius. In other words, the center is chosen so it is the same distance to every side, which defines the incenter. For contrast, the circumcenter is the center of the circle through the vertices (equidistant from the vertices), the centroid is the balance point where the medians meet, and the orthocenter is where the altitudes intersect.

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