Nine Point Circle
The nine-point circle is a circle that can be constructed for any given triangle and passes through nine significant points defined from the triangle.
1. 3 of those points are the midpoints of the sides of the triangle (here: M).
2. 3 of those points are the feet of the altitudes (here: H). Their intersection is called the orthocenter.
3. 3 of those points are the midpoints of the segments connecting the orthocenter to the points of the triangle (here: N).
To find the center of the nine-point circle you must construct the inner triangle of the original triangle: a second triangle with the midpoints of the sides of the original triangle as it's corner points. Then you must draw lines perpendicular to the sides of the new triangle that go through the midpoints of those sides (X,Y&Z), the Perpendicular Bisectors. Their intersection is then the center of the nine-point circle.