# Wheels within wheels

Three circles, two of them equal, are drawn in contact with a semicircle as shown.

The radius of the semicircle is 12cm. What is the radius of the smallest circle?

BRAINTEASERS SOLUTIONS

The radius of the smallest circle is 3cm. Since the normal to the common tangent at S passes through the centres of the circles, SRB is a straight line. Using Pythagoras' theorem: in triangle RTP, RT2 = (a+b)2 - (a-b)2; in triangle RTB, RT2 = (2a - b)2 - b2; Equating the two expressions for RT2, gives a = 2b, so b = 3cm

It only takes a moment and you'll get access to more news, plus courses, jobs and teaching resources tailored to you

## Latest stories

### Coronavirus and schools: LIVE 26/10

A one-stop shop for teachers who want to know what impact the ongoing pandemic will have on their working lives
Tes Reporter 26 Oct 2020

### WATCH: Tips for embedding wellbeing at your school

Join Matt Seddon as he explains how his school in Hong Kong has made staff and student wellbeing a priority
Tes Editorial 25 Oct 2020

The way you park your car at school in the morning says a lot about your approach to the job, says Stephen Petty
Stephen Petty 25 Oct 2020

### Do teachers cry more than people in other professions?

Are teachers more likely to cry in the workplace because they're naturally empathic? Or, says Zoe Enser, is it a reflection on the job itself?
Zoe Enser 25 Oct 2020

### Class book review: Wink

This account of cancer – based on the author's experiences – made our reviewers cry, laugh and keep turning the pages
Gill Ward 25 Oct 2020

### Experts call for pupils to wear masks in classrooms

Independent Sage group calls for secondary school pupils to wear masks in classrooms for up to four weeks after a circuit breaker lockdown
John Roberts 25 Oct 2020

### Labour to push for new vote on free school meals

Sir Keir Starmer tells government its 'not to late to do the right thing' after impact of Marcus Rashford's campaign
John Roberts 25 Oct 2020

### 9 tips for surviving quarantine and staying sane

Two weeks in a hotel room is no one's idea of fun - but there are some ways to make it more bearable, as this recently freed teacher outlines
Chris Barnes 25 Oct 2020

### Schools may have to partially close, says top scientist

Professor Neil Ferguson warns that country may be unable to 'get on top of Covid transmission' without moving to virtual education
John Roberts 25 Oct 2020

### GCSEs: Why we should hold a second exam series in July

Running a second GCSE English and maths exam series in July would benefit post-16 students, says Jonny Kay
Jonny Kay 25 Oct 2020