Hagge Circles and Isogonal Conjugation

Let Q be a point on the circumcircle of triangle ABC . The reflections of Q in the three triangle sides are known to be collinear, and the line thus defined contains the orthocentre H . This fact can form the basis of a proof of the existence of the Simson line, or alternatively can be deduced from the existence of the Simson line by enlarging the Simson line by a factor of 2 from the centre Q .