# What is the 9 point circle used for?

## What is the 9 point circle used for?

A nine-point circle bisects a line segment going from the corresponding triangle’s orthocenter to any point on its circumcircle.

How do you find the 9 point circle?

One way to find the center of the nine point circle (O) is to find the midpoint f the segment that connects the orthocenter (H) and the circumcenter (N), which is the intersection point of the perpendicular bisectors of each side of the original triangle.

### What is the Centre of nine-point circle?

The nine-point center is the circumcenter of the medial triangle of the given triangle, the circumcenter of the orthic triangle of the given triangle, and the circumcenter of the Euler triangle. More generally it is the circumcenter of any triangle defined from three of the nine points defining the nine-point circle.

What is a point circle?

(iii) If g2 + f2 – c = 0 then the radius of the circle becomes zero. In this case, the circle reduces to the point (-g, -f). Such a circle is known as a point circle. In other words, the equation x2 + y2 + 2gx + 2fy + c = 0 represents a point circle. Such a circle is called an imaginary circle.

#### What is radius of nine-point circle?

Consequently, the radius of the nine-point circle is exactly half the circumradius of the triangle: r N = 1 2 R .

Who discovered the 9 point circle?

Karl Wilhelm Feuerbach
In 1765, the eminent Swiss-born mathematician Leonhard Euler showed that nine points constructed from a triangle lie on a circle. This circle would come to be called the Feuerbach circle after Karl Wilhelm Feuerbach, a professor at the gymnasium in Erlangen, Germany.

## What is a nine-point circle class 9?

The nine-point circle, also called Euler’s circle or the Feuerbach circle, is the circle that passes through the perpendicular feet , , and dropped from the vertices of any reference triangle on the sides opposite them.

Who discovered the nine-point circle?

### What is the radius of point circle?

The distance from a circle’s center to a point on the circle is called the radius of the circle. A radius is a line segment with one endpoint at the center of the circle and the other endpoint on the circle. For the circle below, AD, DB, and DC are radii of a circle with center D.

What is the circle formula?

We use the circle formula to calculate the area, diameter, and circumference of a circle. The length between any point on the circle and its center is known as its radius….Formulas Related to Circles.

Diameter of a Circle D = 2 × r
Circumference of a Circle C = 2 × π × r
Area of a Circle A = π × r2

#### How many nine point circles Can a triangle have?

Furthermore, the three points on the nine-point circle that touch the excircles form the vertices of the Feuerbach triangle (Kimberling 1998, p. 158). Given four arbitrary points, the four nine-points circles of the triangles formed by taking three points at a times are concurrent (Lemoine 1904; Wells 1991, p.

How many circles are determined by nine points?

Finally, the point of concurrence of the four nine-points circles is also the point of concurrence of the four circles determined by the feet of the perpendiculars dropped from each of the four points onto the sides of the triangle formed by the other three (Schröder 1999).