In the figure given below, AB ∥ DE, AC = 3cm, CE = 7.5cm and BD = 14cm. Calculate CB and DC.

In the figure (1) given below, AP = 2PB and CP = 2PD.

(i) Prove that △ACP is similar to △BDP and AC ∥ BD.

(ii) If AC = 4.5 cm, calculate the length of BD.

In the figure (ii) given below, ∠ADC = ∠BAC. Prove that CA² = DC × BC.

In the figure (2) given below, CA ∥ BD, the lines AB and CD meet at O.

(i) Prove that △ACO ~ △BDO.

(ii) If BD = 2.4 cm, OD = 4 cm, OB = 3.2 cm and AC = 3.6 cm, calculate OA and OC.