Take an arbitrary triangle ABC. Construct the midpoints of its sides. Construct its altitudes, the altitudes concur at a point H, called the orthocenter. Then construct the midpoints of the segments joining H to the triangle's vertices.

When we draw a circle through the midpoints of sides, we see that it also passes through six other points we've constructed. This circle is named after the great swiss mathematician Leonhard Euler. Another frequently used name is the nine-point circle.

Drag the vertices and make sure that the circle always passes through the nine points we have constructed.