Geometry

Question Analysis

The main focus is to recall the properties of different centers of a triangle and determine which one corresponds to the intersection of perpendicular bisectors.

Key Concept Explanation

Circumcenter: It is the point where the three perpendicular bisectors of a triangle's sides meet. It's equidistant from all vertices of the triangle and serves as the center of the circum - circle (the circle passing through the triangle's vertices).

Orthocenter: Intersection point of the three altitudes of a triangle.

Incenter: Intersection of the three angle bisectors, equidistant from the triangle's sides and center of the in - circle.

Centroid: Intersection of the three medians (lines from vertices to mid - points of opposite sides).

Step-by-Step Solution

By definition, the intersection of the three perpendicular bisectors of a triangle is the circumcenter.

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