ADDITIONAL MATHEMATICS 4037 · STRUCTURED PRACTICE
Paper 2 · Calculator1
The diagram shows a circle with centre and radius . Two straight line tangents and are drawn from an external point to touch the circle at points and respectively. The angle between the tangents is .
(a)
[2]Show that the central angle , and determine the exact length of the tangent segment .
(b)
[3]Calculate the exact perimeter of the shaded region bounded by the tangent segments , and the minor arc .
(c)
[5]Calculate the exact area of the shaded region bounded by the tangents , and the minor arc .
Total: 10 marks