Question 563454
Statements a) and b) cannot be true, since it is possible to find counterexamples for each one. Note that a cyclic quadrilateral is a quadrilateral whose four vertices all lie on a circle.


For statement a), a "kite" shape formed by taking a right triangle and reflecting it about the hypotenuse is a counterexample, since such a quadrilateral is cyclic and not every kite shape will have diagonals that bisect each other.


For statement b), a parallelogram (other than a rectangle) is a counterexample, because its diagonals bisect each other, but parallelograms (other than rectangles) *cannot* be cyclic (since opposite angles must add to 180).