The Nine-Point Circle

A surprise hidden in every triangle

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Side midpoints, altitude feet and midpoints to the orthocentre: nine points on one circle.
• Its radius is half the circumradius.
• Its centre is the midpoint of O and H on Euler’s line.

Steps

1. Nine points, one circle
2. Drag the corner
3. An equilateral triangle
4. A right triangle
5. Touching circles
6. On Euler’s line