# The Euler Line and the Nine Point Circle

- Author:
- Julie Buasen

- Topic:
- Centroid or Barycenter, Circle, Orthocenter

## The orthocenter,the centroid and the circumcenter of a non-equilateral triangle are aligned; that is to say, they belong to the same straight line, called line of Euler. In any triangle, the mid-points of its sides, the feet of its altitudes, and the mid

1. A triangle has how many, nine-point circles? Euler lines?
2. In general, a triangle and its nine-point circle have how many points in common?
3. Give the maximum and minimum number of points a triangle and its nine-point circle might have in common?