RO-NMO 2003 Problem 101

Let be a tetahedron $OABC$ with $OA\perp OB\perp OC\perp OA.$ Show that $$OH\le r\left( 1+\sqrt 3 \right) ,$$ where $H$ is the orthocenter of $ABC$ and $r$ is radius of the inscribed spere of $OABC.$ Valentin Vornicu