8 OYC is a triangle. A is a point on OY and B is a point on CY. AB is parallel to OC. AC and OB intersect at X. (a) Prove that triangle ABX is similar to triangle COX. Give a reason for each statement you make. (b) OA = 3a and OC = 6c and CB : BY = 1 : 2 . Find, as simply as possible, in terms of a and/or c (i) AB, (ii) CY . (c) Find, in its simplest form, the ratio (i) OX : XB, (ii) area of triangle COX : area of triangle ABX, (iii) area of triangle AYB : area of trapezium OABC.