*Vladimir Nikolin*

There are several proofs of the concurrency of the altitudes, this is yet another one.

As we know, if point F is antipode of the vertex C, so that CF is a diameter of the circumcircle of the triangle ABC and H is intersection of the two altitudes h_{a} and h_{b} to the sides a and b,

Attach:Geometry/altitudes.png Δ| **CH is parallel to OM _{c}**

then (corollary 2), the triangle CFH has midline OM_{c}, **CH is parallel to OM _{c}**.

Line OM_{c} is the perpendicular bisector of the side AB, which means that OM_{c} \perp AB , so also CH \perp AB. Q.E.D.