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Orthocenter

Definition of Orthocenter

The point of intersection of the altitudes of a triangle is called an orthocenter.

More about Orthocenter

Orthocenter of an obtuse triangle lies outside the triangle.
Orthocenter of an acute triangle lies inside the triangle.
Orthocenter of a right triangle lies on the triangle.

Example of Orthocenter

In the figure, AD, BE, and CF are the altitudes drawn from the vertices A, B, and C respectively. The point of intersection of these altitudes is 'H'. So, 'H' is the orthocenter of the triangle ABC.

Solved Example on Orthocenter

In a right-angled triangle, the orthocenter lies
Choices:
A. at the vertex containing the right angle
B. outside the triangle
C. at the midpoint of the hypotenuse
D. inside the triangle
Correct Answer: A
Solution:
Step 1: 

Step 2: Orthocenter is the point of intersection of the altitudes. Each leg in a right triangle forms an altitude.
Step 3: So, in a right-angled triangle, the orthocenter lies at the vertex containing the right angle.

Related Terms for Orthocenter

Altitude
Point of Intersection
Triangle