What is a ninepoint circle List the 9 points of the ninepoin

What is a nine-point circle? List the 9 points of the nine-point circle of a triangle. Can a triangle have more than one nine-point circle? Why or why not? What is the radius and where is the center of the nine-point circle of a triangle?

Solution

The nine-point circle, also called euler\'s circle, is the circle that passes through the feet of the perpendiculars to the sides from the opposite vertices H_A, H_B, and H_C in the triangle with vertices A, B, and C. It passes through the midpoints M_A, M_B, and M_C of the sides of the triangle, and also passes through the midpoints E_A, E_B, and E_C of the line segments joining orthocenter to the vertices of the Triangle.

A triangle Cannot have more than one nine-point circle.

Center of the nine-point circle bisects the circumcenter and orthocenter.

The radius of nine-point circle is half the radius of Circumcircle.