[Figure showing a circle, centre O, with points A, B, C, D on the circumference. AOD and OCE are straight lines. DE is a tangent to the circle at D. Angle ABC = 126° and DE = 10.5 cm. Labelled 'NOT TO SCALE'.] A, B, C and D are points on a circle, centre O. AOD and OCE are straight lines. DE is a tangent to the circle at D. Angle ABC = 126° and DE = 10.5 cm. Calculate the radius of the circle.

1. (a)[Figure showing a circle, centre O, with points A, B, C, D on the circumference. AOD and OCE are straight lines. DE is a tangent to the circle at D. Angle ABC = 126° and DE = 10.5 cm. Labelled 'NOT TO SCALE'.] A, B, C and D are points on a circle, centre O. AOD and OCE are straight lines. DE is a tangent to the circle at D. Angle ABC = 126° and DE = 10.5 cm. Calculate the radius of the circle.[5]
2. (b)[Figure showing a circle, centre O, with points P and Q on the circumference. Angle POQ = 82°. Labelled 'NOT TO SCALE'.] P and Q are points on a different circle, centre O. The angle of the minor sector POQ is 82°. The length of the minor arc PQ is 7.3 cm. Calculate the area of the major sector.[5]

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