Question

question 19 of 25 the ______ of a triangle is the center of the only circle that can be circumscribed about it. a. circumcenter b. incenter c. altitude

Explanation:

• Recall the definitions:
• The circumcenter of a triangle is the point where the perpendicular bisectors of the sides intersect. This point is equidistant from all three vertices of the triangle, and it is the center of the circumscribed circle (circumcircle) around the triangle.
• The incenter is the center of the inscribed circle (incircle) and is the intersection of angle bisectors, so it's not for the circumscribed circle.
• An altitude is a perpendicular segment from a vertex to the opposite side, not a center of a circle.

So the correct term for the center of the circumscribed circle about a triangle is the circumcenter.

Answer:

A. circumcenter