### Review question R6838 at the Circles station

Two coplanar circles, each of radius \(\quantity{5}{cm}\), have their centres \(\quantity{6}{cm}\) apart. Calculate the area of the region common to the interiors of both the circles, giving your answer in \(\mathrm{cm}^2\) correct to two significant figures.

### Using this Review question

This problem requires students to work out what is happening (ideally by drawing a sketch of the situation) and then to devise a strategy for solving the question asked. This could be used either before or after introducing radians.

It could be used to **introduce the idea** of calculating areas of sectors and segments; by asking students to generalise their results, they could derive these formulae for themselves. It could also be used at some point after learning this skill as a **review** of these skills.

A **related problem** could be to work out the perimeter of the common region.

The question could also be **generalised** to ask how the answer would change if the numbers in the question were changed.

### Aspects of mathematical thinking

**Mathematical behaviours to look out for**Devising a strategy to enter the problem

Drawing appropriate sketches: marking appropriate lengths and angles on the diagram

Recognising which triangle techniques are needed (Pythagoras, appropriate trigonometry)

Making use of proportion to calculate sector areas

**Overarching ideas**Pervasive idea: Symmetry (offering a way into the problem)

Proportional reasoning