## Proof Without Words: Nine-Point Circle Property

The “Nine-Point Circle” of a triangle $$\triangle ABC$$ contains the vertices of the medial triangle ($$\triangle RST$$) and orthic triangle ($$\triangle UVW$$), as well as points $$X$$, $$Y$$, $$Z$$ that bisect segments from $$\triangle ABC$$’s orthocenter ($$H$$) to its vertices.

A question on Math.StackExchange.com asked for proof that the center of the nine-point circle bisects the segment joining orthocenter $$H$$ and circumcenter $$O$$. I thought I’d post my answer here.