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. GÔX = y°. [Figure with two circles, points, lines, angles]

1. (a)(i)Find each of these angles, as simply as possible, in terms of y. Give reasons for your answers. GÊO[2]
2. (a)(ii)GĈX[2]
3. (a)(iii)DÂB[2]
4. (b)Complete the sentence. Triangle EGC is congruent to triangle ....................[1]
5. (c)Prove that triangle ADC is similar to triangle OGC. Give a reason for each statement you make.[2]
6. (d)What special type of quadrilateral is AOGD?[1]
7. (e)(i)Find the ratio area of triangle OGC : area of triangle ADC,[1]
8. (e)(ii)Find the ratio area of triangle OGC : area of quadrilateral ABCD.[1]

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