How to Find the Orthocenter of a Triangle | Steps and Properties

orthocenter

The orthocenter is a point in a triangle where all three altitudes intersect

The orthocenter is a point in a triangle where all three altitudes intersect. An altitude is a line segment drawn from one vertex of a triangle perpendicular to the opposite side.

To find the orthocenter of a triangle, you can follow these steps:

1. Draw the triangle and label the vertices as A, B, and C.
2. Construct the perpendicular bisectors of the sides. This can be done by finding the midpoint of each side and drawing a line perpendicular to that side passing through the midpoint.
3. Where two perpendicular bisectors intersect, label the point as O. This is the circumcenter of the triangle.
4. Extend segment AO to pass through point O.
5. The point where segment AO intersects side BC is the orthocenter of the triangle.

It is worth noting that not all triangles have an orthocenter. In an obtuse triangle, one of the altitudes will be outside the triangle, meaning there is no point of intersection.

The orthocenter has several unique properties in a triangle. For example, the orthocenter, circumcenter, and centroid of a triangle are collinear, meaning they lie on the same line called the Euler line. Additionally, the distance between the orthocenter and a vertex of a triangle is equal to twice the distance between the circumcenter and the opposite side.

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