Geometry

Question Analysis

The main focus is to recall the specific point where the altitudes of a triangle intersect among the given geometric centers.

Key Concept Explanation

Orthocenter: It is the point of intersection of the altitudes of a triangle. An altitude is a perpendicular line segment from a vertex to the opposite side.

Circumcenter: The point where the perpendicular bisectors of the sides of a triangle intersect. It is the center of the circum - circle that passes through all three vertices 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.

Incenter: The point where the angle bisectors of a triangle intersect. It is the center of the in - circle that is tangent to all three sides of the triangle.

Step - by - Step Solution

1. Recall the definitions of each geometric center:

A.For the circumcenter, it is related to perpendicular bisectors, not altitudes.

B.The orthocenter is defined as the point where the altitudes of a triangle intersect.

C.The centroid is related to medians, not altitudes.

D.The incenter is related to angle bisectors, not altitudes.

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