Geometry

Question Analysis

The main focus is to identify the name of the center point  in the triangle based on the properties of different triangle centers.

Key Concept Explanation

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

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

Centroid: The point where the medians of a triangle intersect. A median is a line segment joining a vertex to the mid - point of the opposite side.

Orthocenter: The point where the altitudes of a triangle intersect. An altitude is a perpendicular line segment from a vertex to the opposite side (or its extension).

In the given figure, the lines are drawn from each vertex to the mid - point of the opposite side, so these are medians.

Step - by - Step Solution

1. Observe the lines in the triangle.

Notice that the lines , , and  connect each vertex (

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