Geometry

Question Analysis

This question delves into the Triangle Perpendicular Bisector Concurrence Theorem. The prime focus is to identify the correct name of the point of concurrency formed by the perpendicular bisectors of a triangle.

Key Concept Explanation

1. Perpendicular bisectors: A perpendicular bisector of a side of a triangle is a line that is perpendicular to the side and passes through its mid - point. According to the Triangle Perpendicular Bisector Concurrence Theorem, the perpendicular bisectors of the sides of a triangle intersect at a single point.

2. Points of concurrency in a triangle: Different sets of lines in a triangle (medians, angle bisectors, altitudes, perpendicular bisectors) intersect at specific points of concurrency, each with its own name and properties.

Step-by-Step Solution

1. Recall the properties associated with each type of point of concurrency in a triangle.

2. Eliminate the options that do not pertain to perpendicular bisectors. The centroid is formed by the intersection of medians, the incenter by angle bisectors, and the orthocenter by altitudes.

3. Identify that the circumcenter is formed by the intersection of perpendicular bisectors.

Option Analysis

A. Centroid: Incorrect. The centroid is the point of concurrency of the medians of a triangle. A median connects a vertex to the mid - point of the opposite side, not a perpendicular bisector.

B. Incenter: Incorrect. The incenter is the point of concurrency of the angle bisectors of a triangle. Angle bise...