CIE/GCE/AS/Math/P1/19/Nov/13/Q#4
Question
The diagram shows a semicircle ACB with centre O and radius 𝑟. Arc OC is part of a
circle with centre A.
(i) Express angle CAO in radians in terms of 𝜋.
(ii) Find the area of the shaded region in terms of 𝑟, 𝜋 and √3, simplifying your
answer.
Solution
(i)
We are required to find the expression for angle CAO in terms of 𝜋.
Consider the diagram below.
It is evident that CAO makes an equilateral triangle.
Question
The diagram shows a semicircle ACB with centre O and radius 𝑟. Arc OC is part of a
circle with centre A.
(i) Express angle CAO in radians in terms of 𝜋.
(ii) Find the area of the shaded region in terms of 𝑟, 𝜋 and √3, simplifying your
answer.
Solution
(i)
We are required to find the expression for angle CAO in terms of 𝜋.
Consider the diagram below.
It is evident that CAO makes an equilateral triangle.
