Category:Nine Point Circle Theorem

This category contains pages concerning Nine Point Circle Theorem:

Let $\triangle ABC$ be a triangle.

These $9$ points:

the feet of the altitudes of $\triangle ABC$

the midpoints of the sides of $\triangle ABC$

the midpoints of the lines from the vertices of $\triangle ABC$ to the orthocenter $H$ of $\triangle ABC$

all lie on the circumference of a circle.

The center $M$ lies on the Euler line of $\triangle ABC$, at the midpoint between the orthocenter $H$ and the circumcenter $O$.