Wheels within wheels

9th January 2004 at 00:00
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

Log-in as an existing print or digital subscriber

Forgotten your subscriber ID?


To access this content and the full TES archive, subscribe now.

View subscriber offers


Get TES online and delivered to your door – for less than the price of a coffee

Save 33% off the cover price with this great subscription offer. Every copy delivered to your door by first-class post, plus full access to TES online and the TES app for just £1.90 per week.
Subscribers also enjoy a range of fantastic offers and benefits worth over £270:

  • Discounts off TES Institute courses
  • Access over 200,000 articles in the TES online archive
  • Free Tastecard membership worth £79.99
  • Discounts with Zipcar, Buyagift.com, Virgin Wines and other partners
Order your low-cost subscription today