Lines that are tangent to a circle are perpendicular to the radius at the point of tangency. A diameter is formed by two radii that go in opposite directions from the center of the circle. It is a straight line because the angle would be 180 degrees. Since the tangent lines are perpendicular, the angles between the radii and tangent lines are 90 degree. Since the diameter is a straight line, it is now a transversal line cutting across the two tangents. The alternate interior angles are equal, they are both 90 degrees. When a transversal cuts two lines and forms equal alternate interior angles, the two lines are parallel.