Geometry

Question Analysis

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

Key Concept Explanation

Circumcenter: The intersection point of the perpendicular bisectors of a triangle's sides. It is equidistant from the vertices and is the center of the circum - circle passing through the vertices.

Incenter: The intersection point of the angle bisectors of a triangle. It is equidistant from the sides and is the center of the incircle tangent to the sides.

Centroid: The intersection point of the medians (lines connecting vertices to the mid - points of opposite sides).

Orthocenter: The intersection point of the altitudes (perpendicular lines from vertices to opposite sides).

Step - by - Step Solution

1. Observe the red arcs in the diagram. 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 point where the angle bisectors of a triangle intersect. Since the lines in the image are angle bisectors, the center shown is the incenter.

Option Analysis

A.Circumcenter: Incorrect. Perpendicular bisectors (not shown here) intersect at the circumcenter.

B.Incenter: Correct. As the lines in th...