# Feuerbach's Theorem

The

The nine-point circle is also called Euler's circle or the Feuerbach circle.

Feuerbach also proved the ninepoint circle was tangent to the three

**nine-point circle**of a given triangle contains the midpoint of each side of the triangle, the foot of each altitude and the midpoint of the line segment from each vertex of the triangle to the orthocenter.The nine-point circle is also called Euler's circle or the Feuerbach circle.

**Feuerbach's Theorem**states that the nine-point circle and the**incircle**of the triangle are mutually tangent (and touch at the**Feuerbach point**).Feuerbach also proved the ninepoint circle was tangent to the three

**ex-circles**of the triangle.