Geometry

Question Analysis

The main focus is on understanding the properties of the circumcenter and recalling the lines that intersect to form it. We need to match the correct type of line segment with the fact that is the circumcenter.

Key Concept Explanation

Perpendicular Bisectors: The perpendicular bisector of a side of a triangle is a line that is perpendicular to the side and passes through its mid - point. The circumcenter is defined as the point of intersection of the three perpendicular bisectors of the sides of a triangle. It is equidistant from all three vertices of the triangle.

Angle Bisectors: These are lines that divide an angle of a triangle into two equal parts. The point of intersection of the angle bisectors is called the incenter.

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

Centroids: A centroid is formed by the intersection of the three medians of a triangle. A median is a line segment joining a vertex to the mid - point of the opposite side.

Step-by-Step Solution

Since

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