8 The diagram shows two circles each with centre O. A, B, C and D are points on the circumference of the large circle. E, F and G are points on the circumference of the small circle. CGD and CFB are tangents to the small circle. Lines AEOC and FG intersect at 90° at X. GOXˆ = y°. (a) Find each of these angles, as simply as possible, in terms of y. Give reasons for your answers. (i) GEOˆ. (ii) GCXˆ. (iii) DABˆ. (b) Complete the sentence. Triangle EGC is congruent to triangle. (c) Prove that triangle ADC is similar to triangle OGC. Give a reason for each statement you make. (d) What special type of quadrilateral is AOGD? (e) Find the ratio (i) area of triangle OGC : area of triangle ADC, (ii) area of triangle OGC : area of quadrilateral ABCD.