Suppose that is a cyclic quadrilateral. Let and . Denote by and the orthocenters of triangles and , respectively. Prove that the points , , are collinear.

Original formulation:

Let be a triangle. A circle passing through and intersects the sides and again at and respectively. Prove that , and are concurrent, where and are the orthocentres of triangles and respectively.

Original formulation:

Let be a triangle. A circle passing through and intersects the sides and again at and respectively. Prove that , and are concurrent, where and are the orthocentres of triangles and respectively.