Geometry

Question Analysis

The main focus is on recalling the concept related to the intersection of the three perpendicular bisectors of a triangle. We need to identify the correct term among the given options.

 

Key Concept Explanation

Circumcenter: It is the point where the three perpendicular bisectors of a triangle intersect. The circumcenter is equidistant from all the vertices of the triangle, and it serves as the center of the circum - circle (the circle that passes through all three vertices of the triangle).

 

Orthocenter: This is the point of intersection of the three altitudes of a triangle. An altitude is a perpendicular line segment from a vertex to the opposite side (or its extension).

 

Incenter: The incenter is the point where the three angle bisectors of a triangle meet. It is equidistant from all the sides of the triangle and is the center of the in - circle (the circle that is tangent to all three sides of the triangle).

 

Centroid: The centroid is the point of intersection of the three medians of a triangle. A median is a line segment that joins a vertex to the mid - point of the opposite side.

 

Step-by-Step Solution

By the definition of the circumcenter, which is specifically the intersection of the three perpendicular bisectors of a triangle, the correct answer is "Circumcenter".

 

Option Analysis

A.Incenter: Incorrect. It is the intersection of angle bisectors, not perpendicular bisectors.

B.Centr...