Geometry

Question Analysis

This question focuses on identifying the type of triangle center represented by point in the given diagram, testing knowledge of different triangle centers.

Key Concept Explanation

Circumcenter: The point of intersection of the perpendicular bisectors of a triangle's sides. It is the center of the circumcircle, which passes through all the vertices of the triangle.

Orthocenter: The point of intersection of the altitudes of a triangle. Altitudes are perpendicular lines from each vertex to the opposite side.

Centroid: The point of intersection of the medians of a triangle. Medians connect each vertex to the mid - point of the opposite side.

Incenter: The point of intersection of the angle bisectors of a triangle. It is the center of the incircle, which is tangent to all the sides of the triangle.

Step - by - Step Solution

1. Observe the diagram. The circle centered at is tangent to all the sides of the triangle.

2. Recall that the incenter is the center of the incircle, which is tangent to the sides of the triangle. Since the circle centered at is tangent to the sides, point

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