Question

the ______ of a triangle is the center of the only circle that can be inscribed inside it.

a. incenter

b. circumcenter

c. altitude

Explanation:

• Recall the definitions:
• The incenter of a triangle is the point where the angle bisectors of the triangle intersect. It is equidistant from all sides of the triangle, and this distance is the radius of the incircle (the circle inscribed inside the triangle).
• The circumcenter is the center of the circumscribed circle (circumcircle) around the triangle, which passes through the vertices, not related to the inscribed circle.
• An altitude is a perpendicular segment from a vertex to the opposite side (or its extension), not a center of a circle.

So the incenter is the center of the inscribed circle in a triangle.

Answer:

A. incenter