What is the nine-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?

Nine Point Circle

1. Mark the midpoints of each side (3 points). See Figure 1.
2. Drop an altitude from each vertex to the opposite side, and mark the points where the altitudes intersect the opposite side.
3. Notice that the altitudes intersect at a common point.

What is nine-point circle Centre?

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 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.

Who invented the nine-point circle?

Feuerbach
The nine-point circle, discovered by Feuerbach in about 1820, contains the midpoints of the three sides of the triangle and the feet of the three altitudes. Its center is the midpoint of the segment joining the orthocenter and the circumcenter of the triangle, and consequently lies on the Euler line.

How many circles are determined by nine points?

four nine
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).

Who discovered nine-point circle?

Who discovered the nine-point circle?

What is a point circle?

A point circle has radius zero and only includes a single point – the centre of the circle. A real/imaginary circle concerns whether the radius of the circle is real or imaginary. If the radius of a circle is imaginary then there are no real points on the circle.

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.

What is the historical background of nine-point circle?

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 in geometry?

The nine-point circle of a triangle is a circle going through 9 key points: the three midpoints of the sides of the triangle (blue in the below picture), the three feet of the altitudes of the triangle (yellow in the below picture), and the three midpoints from the vertices to the orthocenter of the triangle (green in the below picture).

What is the 9 point circle?

In geometry, the nine-point circle is a circle that can be constructed for any given triangle . It is so named because it passes through nine significant concyclic points defined from the triangle.

What are nine circles?

Nine Circles is a Dutch-German minimal electronic band. The name originates from the “Nine Circles of Hell” from Dante Alighieri’s “Divine Comedy”.