2 (a) A, B, C and D are points on the circumference of the circle and AC is a diameter. AFBE and DCE are straight lines. DF is perpendicular to AE and CDFˆ = 67°. (i) Find AEDˆ. (ii) Find CBEˆ, giving a reason for your answer. (iii) Explain why DF is parallel to CB. (b) In the triangle PQR, the bisectors of PQRˆ and PRQˆ intersect at Y. The straight line XYZ is parallel to QR. Prove that the perimeter of triangle PXZ = PQ + PR.