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.