Geometry

Question Analysis

This question focuses on understanding the intersection point (orthocenter) of the altitudes in an obtuse - angled triangle. The key is to recall the properties of altitudes in different types of triangles.

Key Concept Explanation

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

In an acute triangle, all altitudes are inside the triangle, and the orthocenter lies inside the triangle.

In a right triangle, the two legs are altitudes, and the orthocenter is at the vertex of the right angle.

In an obtuse triangle, the altitudes from the acute - angled vertices need to be extended outside the triangle to meet the opposite sides (or their extensions). As a result, the orthocenter lies outside the triangle.

Step - by - Step Solution

1. Analyze the properties of an obtuse triangle:

In an obtuse triangle, one of the angles is greater than