The point of concurrency of the three angle bisectors, equidistant from each side of the triangle, and the center of the incircle is called?

• A. Incenter
• B. Circumcenter
• C. Centroid
• D. Orthocenter

Answer: (A)

The point where the angle bisectors meet is the center of the incircle, and it is equidistant from all three sides. An angle bisector consists of points that are the same distance from the two sides that form that angle, so when all three bisectors intersect, that single point is equally distant from each side. That common distance is the radius of a circle drawn with this point as center that just touches all three sides—the incircle. This is why the name for this center is the incenter. The other centers have different meanings: the circumcenter is the point equally distant from the triangle’s vertices, the centroid is the intersection of the medians, and the orthocenter is the intersection of the altitudes.