(a) Let ABCD be a quadrilateral inscribed in a circle. If |AB| = |CD|, prove that BC is parallel to DA (i.e., ABCD is a trapezoid).

(b) Prove that if a trapezoid is inscribed in a circle, it is an isosceles trapezoid.

(c) Prove that if a parallelogram is inscribed in a circle, it is a rectangle.