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In short, the orthocenter really has no purpose.
There are 4 points of Concurrency in Triangles:
1) The Centroid - the point of concurrency where the 3 medians of a triangle meet. This point is also the triangle's center of gravity.
2) The Circumcenter - the point of concurrency where the perpendicular bisectors of all three sides of the triangle meet. This point is the center of the triangle's circumscribed circle.
3) The Incenter - the point of concurrency where the angle bisectors of all three angles of the triangle meet. Like the circumcenter, the incenter is the center of the inscribed circle of a triangle.
4) The Orthocenter - the point of concurrency where the 3 altitudes of a triangle meet. Unlike the other three points of concurrency, the orthocenter is only there to show that altitudes are concurrent. Thus, bringing me back to the initial statement.
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How do you find orthocenter?
You find the orthocenter by constructing the altitudes from the vertices in a triangle. If the triangle is obtuse, the orthocenter will fall outside the triangle. If the triangle is acute, the orthocenter will fall on the inside of the triangle. If the triangle is a right triangle, the orthocenter will lie on a vertix.
Why is there a orthocenter?
There just is :)In all seriousness, all triangles (by definition) have an orthocenter and other points of concurrency. The definitions of an orthocenter is the place where the altitudes of all three sides intersect.
What is the intersection of the three altitudes of a triangle?
orthocenter
What is the use of a orthocenter?
The orthocenter is the point of concurrency of the altitudes in a triangle. A point of concurrency is the intersection of 3 or more lines, rays, segments or planes. The orthocenter is just one point of concurrency in a triangle. The others are the incenter, the circumcenter and the centroid.My daughter's math teacher recommended the following site, which was enormously helpful for her. Here's a link to the 'orthocenter' topic, and you can find a bunch of other math topic videos there. It is all free. Hope it will help.http://www.brightstorm.com/d/math/s/geometry/u/constructions/t/constructing-the-orthocenter
Where is the orthocenter of a right triangle?
At the vertex of the right angle.
