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*?

**Teacher notes:**

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.

**Solutions:**

You can download a pdf of the solution here.

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