Maths with David

    9709. P1. Circular Measure. Past Exam Questions

    November 2025 (9709/12). Question 10

    The diagram above shows a circle with centre A and radius r passing through points B, C and D. A larger circle of radius s has centre C and passes through B and D. The length BD is also s.

    (a) Show that s = \sqrt{3} r [2 marks]

    (b) Find an expression for the area of the shaded region. Give your answer in the form (a + b \pi) r^2 , where a and b are constants to be found [7 marks]

    9709/11/M/J/25q9 – Mark Scheme

    The diagram shows a sector ABC of a circle with centre A and radius r cm. The angle BAC is \alpha radians, where 0 < \alpha < \frac{1}{2} pi .

    (a) It is given that the area of the triangle ABC is 4cm2 and the area of the sector ABS is 8 \alpha cm^2 .

    Find the exact area of the shaded segment. [4 marks]

    (b) It is given instead that the length of the chord BC is \frac{1}{ \sqrt{2} } r cm but the area of the triangle ABC is still 4cm2.

    Find the area of the shaded segment. Give your answer correct to 3 significant figures. [4 marks]

    9709/12/M/J/25q8 (includes significant amounts of coordinate geometry)