What are the 9 points of a 9 point circle?
These nine points are:
- The midpoint of each side of the triangle.
- The foot of each altitude.
- The midpoint of the line segment from each vertex of the triangle to the orthocenter (where the three altitudes meet; these line segments lie on their respective altitudes).
What is the purpose of a 9 point circle?
The nine-point circle bisects any line from the orthocenter to a point on the circumcircle. The incircle and three excircles of a reference triangle are all touched by the nine-point circle.
Who discovered Feuerbach’s nine-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.
How do you find the radius of a 9 point circle?
Consequently, the radius of the nine-point circle is exactly half the circumradius of the triangle: r N = 1 2 R .
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 the center of the nine-point circle?
The center of the nine-point circle, known as the nine-point center N N N, lies on the Euler line of the triangle, and is the midpoint of the section of the Euler line from the orthocenter H H H to the circumcenter O O O.
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 radius of nine-point circle?
The circle constructed passes through 3 concyclic points from the triangle. The center of it lies at the nine-point center of the triangle, and the radius of the nine-point circle is exactly half of the circumradius of the triangle that is N = 1/2R.
What is an oiler triangle?
The Euler triangle of a triangle is the triangle whose vertices are the midpoints of the segments joining the orthocenter. with the respective vertices. The vertices of the triangle are known as the Euler points, and lie on the nine-point circle.
What is centroid Class 9?
The centroid is the centre point of the object. The point in which the three medians of the triangle intersect is known as the centroid of a triangle. It is also defined as the point of intersection of all the three medians.
What is circum Centre?
Definition of circumcenter : the point at which the perpendicular bisectors of the sides of a triangle intersect and which is equidistant from the three vertices.
Is centroid a formula?
Then, we can calculate the centroid of the triangle by taking the average of the x coordinates and the y coordinates of all the three vertices. So, the centroid formula can be mathematically expressed as G(x, y) = ((x1 + x2 + x3)/3, (y1 + y2 + y3)/3).
Is orthocentre and circumcentre same?
Circumcenter is created using the perpendicular bisectors of the triangle. Incenters is created using the angles bisectors of the triangles. Orthocenter is created using the heights(altitudes) of the triangle.