A shape is formed as follows:
A circle is drawn such that the points A, B, C, D are equally spaced around the circumference. The arcs AB and CD are reflected in the lines AB and CD respectively.
This makes the following shape:
(a) Find the area of the shaded shape when the radius, r, of the original circle is 1.
(b) What is the area of the shaded shape when r = a?
Level of difficulty: Accessible for SL and HL students
Syllabus knowledge required: Sectors and segments
This would be a good starter which can be done as a non-calculator exercise.
You can download a pdf of the solution here.