Wheels within wheels

Tes Editorial

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?


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

Register to continue reading for free

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

Tes Editorial

Latest stories

Class book review: Wink by Rob Harrell

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