10 The diagram shows two circles that touch at C. A, B and C are points on the small circle, centre X. C, D and E are points on the large circle, centre Y. AXCYE and BCD are straight lines and YDEˆ = x°. (a) Prove that triangle BCX is similar to triangle DCY. Give a reason for each statement you make. (b) Find, in terms of x, (i) DCYˆ , (ii) BXAˆ. (c) Given that BC = 3.5 cm, CX = 3.2 cm and CD = 5.6 cm, find the length of AE.