Geometry

Question Analysis

This question focuses on identifying the special segments that intersect to form the incenter of a triangle, testing knowledge of triangle - related line segments.

Key Concept Explanation

Medians: Line segments that connect a vertex of a triangle to the mid - point of the opposite side. Their intersection point is the centroid.

Altitudes: Perpendicular line segments from a vertex to the opposite side (or its extension). Their intersection point is the orthocenter.

Angle Bisectors: Line segments that divide an angle of a triangle into two equal - measure angles. Their intersection point is the incenter.

Perpendicular Bisectors: Line segments that are perpendicular to a side of a triangle and bisect it. Their intersection point is the circumcenter.

Step - by - Step Solution

1. Recall the definitions of each type of special segment in a triangle.

2. Recognize that the incenter is defined as the point where the angle bisectors of a triangle meet.

Option Analysis

A.Medians: Incorrect. Medians intersect at the centroid.

B.Altitudes: Incorrect. Altitudes intersect at the orthocenter.

C.Angle Bisectors: Correct. Angle bisectors intersect at t...