Geometry

Question Analysis

This question focuses on identifying the center of a triangle depicted in the image, testing knowledge of different triangle centers.

Key Concept Explanation

Incenter: The point of intersection of the angle bisectors of a triangle. It is equidistant from the sides of the triangle.

Centroid: The point of intersection of the medians (lines connecting each vertex to the mid - point of the opposite side).

Orthocenter: The point of intersection of the altitudes (perpendicular lines from each vertex to the opposite side).

Circumcenter: The point of intersection of the perpendicular bisectors of the sides of a triangle. It is equidistant from the vertices of the triangle.

Step - by - Step Solution

1. Observe the red arcs in the image. These arcs indicate that the lines are angle bisectors, as they show equal - measure angles at each vertex.

2. Recall that the incenter is defined as the intersection point of the angle bisectors of a triangle. Since the lines in the image are angle bisectors, the center shown is the incenter.

Option Analysis

A.Incenter: Correct. As the lines in the image are angle bisectors, and their intersection is the incenter.

B.Centroid: Incorrect. Medians (not shown here) intersec...