Geometry

Question Analysis

The main focus is to determine the location of the orthocenter in an acute triangle based on the properties of altitudes and the triangle's angles.

Key Concept Explanation

The orthocenter 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. In an acute triangle, all angles are less than 90°.

Step - by - Step Solution

1. Recall the properties of an acute triangle:

In an acute triangle, when we draw the altitudes from each vertex to the opposite side, the lines of the altitudes will intersect inside the triangle. This is because the angles are such that the perpendiculars from the vertices will cross within the boundaries of the triangle.

Option Analysis

A.Outside: Incorrect. In an acute triangle, the orthocenter is not outside the triangle. This is typically the case for an obtuse triangle.

B.Inside: Correct. Since all angles in an acute triangle are less than 90°, the altitudes intersect inside the triangle, making the orthocenter located inside.

C.On the angle: Incorrect. The orthocenter is not on an angle. This would be the case in a right triangle where the orthocenter is at the vertex of the right angle.

D.None ...