# Nine-Point Circle

- Author:
- Corazon Bautista

- Topic:
- Circle

**Nine-point circle**is a circle that contains the following nine points: midpoints of the sides of triangle

*ABC*, feet of the altitudes of triangle

*ABC*, and Euler points of the triangle

*Euler points*of a triangle are the midpoints of the segments joining the orthocenter of a triangle to its vertices.

*Orthocenter*is the point of concurrency of the altitudes of a triangle.

*Altitude*is the segment drawn from a vertex of the triangle perpendicular to the side opposite the vertex. Drag any of the vertices of triangle ABC. Write down your observations as the triangle changes its size. And finally, how do you locate the center of this nine-point circle? (Hint: What is a property of a perpendicular bisector of a chord in a circle that you can use in this case? Recreate the image on Geogebra to discover this property.)