29th October 2004 at 01:00
Use all the numbers: 1, 2, 3, 4, 6 and 8.

(a) Put one number in each circle so that the product of the three numbers on each side of the triangle is 24.

(b) Find another way of putting the numbers in the circles so that the product of the three numbers on each side of the triangle is the same.

P is a point on a sphere of radius 6cm.

A pair of compasses is opened to make a radius of 4cm and a circle with centre P is drawn on the sphere.

(a) What is the radius of the circle?

(b) To what radius must the compasses be opened to draw the largest possible circle with centre P?

SOLUTIONS Equal products Product: 24 Product: 48 Circles on spheres (a) The radius of the circle is 8C23 cm. Using Pythagoras' theorem: r2 = 62 - (6 - a)2 = 42 - a2, giving a = 43 and r = 8C23. (b) The largest circle that can be drawn is round the "equator" of the sphere, when c, the radius of the compasses, is given by: c2 = 62 + 62, or c= 6C2.

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,, Virgin Wines and other partners
Order your low-cost subscription today