Orthocenter

# Orthocenter

## Orthocentre of a Triangle Properties

A triangle has three vertices, or corners, and three sides. The orthocentre is a special point in a triangle that is located at the intersection of the three altitudes. The altitudes are the lines that connect the vertices of a triangle to the opposite side. The orthocentre is also the centre of the triangle’s circumcircle.

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## Orthocenter Definition

The orthocenter of a triangle is the intersection of its three altitudes. It is also the center of the triangle’s nine-point circle.

## Orthocenter Properties

There are three orthocenter properties:

1. The orthocenter is the intersection of the three altitudes of a triangle.

2. The orthocenter is the center of the triangle’s nine-point circle.

3. The orthocenter is also the center of the triangle’s Euler line.

## How to Calculate Orthocenter of a Triangle :

The orthocenter of a triangle is the point where the three altitudes of the triangle intersect. To calculate the orthocenter of a triangle, you need to know the lengths of the three altitudes.

Once you have the lengths of the altitudes, simply use the Pythagorean theorem to calculate the distance from each vertex to the orthocenter. The orthocenter will be the point where the three distances intersect.

## :

1. The American Revolution

2. The Civil War

3. The American Civil Rights Movement

4. The women’s suffrage movement

5. The gay rights movement

## 1. Find the orthocenter of the triangle with the given vertices:

A(-1, 2), B(3, 4), and C(5, -6)

The orthocenter is at the intersection of the three altitudes of the triangle. The altitudes are the lines from a vertex to the opposite side. The three altitudes are:

AB: From A to BC
AC: From A to CB
BC: From B to CA

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