Prove that tangents to a circle at the endpoints of a diameter are parallel?

A tangent to a circle is perpendicular to the radius drawn to the point of tangency. But since the points of tangency are the endpoints of a diameter, the radii to the points of tangency are simply the two halves of that diameter, which means that the diameter is perpendicular to both tangents. And since the two tangents have a common perpendicular, they must be parallel.