# Nine point circle construction

## How do you make a nine point circle?

To construct the nine point circle of a triangle, follow these steps. Draw a triangle ABC. Construct the midpoints of the three sides. Label them as L, M, N. Construct the feet of the altitudes of the triangle ABC. Label them as D, E, F. Construct the midpoints of the segments AH, BH, CH. Label them as X, Y, Z.

## How do you find the center of a nine 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.

Feuerbach

## Why is the nine point circle important?

The nine – point circle created for that orthocentric system is the circumcircle of the original triangle. The feet of the altitudes in the orthocentric system are the vertices of the original triangle.

## 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 different triangles can you get on an N Point Circle?

Possible no of triangles are NC3 as no collinear points on circle . In how many maximum parts a circle can be divided into with 3 straight lines, which intersects the circle exactly at 2 points ?

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## What is Euler’s line used for?

Applications. One important consequence of the Euler line is that information about any one of the centroid, orthocenter, and circumcenter can be derived from information about the other two.

## What is the formula of Circumcentre?

According to the circumcenter properties, the distance of (X, Y) from each vertex of a triangle would be the same. Assume that D1 be the distance between the vertex (x1, y1) and the circumcenter (X, Y), then the formula is given by, D1= √[(X−x1)2+(Y−y1)2] D2= √[(X−x2)2+(Y−y2)2]

## What is Orthocenter of a triangle?

Orthocenter – the point where the three altitudes of a triangle meet (given that the triangle is acute) Circumcenter – the point where three perpendicular bisectors of a triangle meet. Centroid- the point where three medians of a triangle meet.

## What is Circumradius of Triangle?

The circumradius of a cyclic polygon is the radius of the circumscribed circle of that polygon. For a triangle , it is the measure of the radius of the circle that circumscribes the triangle . Since every triangle is cyclic, every triangle has a circumscribed circle, or a circumcircle .

## What is Ninepoint?

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.

## What is circum Centre?

The circumcenter is the center of a triangle’s circumcircle. It can be found as the intersection of the perpendicular bisectors.