Weekly Problem 19 - 2010

Three circles of different radii each touch the other two. What can you deduce about the arc length between these points?

Weekly Problem 34 - 2010

Can you work out the fraction of the larger square that is covered by the shaded area?

Weekly Problem 49 - 2006

What is the area of the shape enclosed by the line and arcs?

Weekly Problem 13 - 2006

If three runners run at the same constant speed around the race tracks, in which order do they finish?

Weekly Problem 36 - 2011

Imagine cutting out a circle which is just contained inside a semicircle. What fraction of the semi-circle will remain?

Weekly Problem 29 - 2014

snail is at one corner of a cube. What proportion of the surface of the cube could the snail reach in one hour?

Weekly Problem 37 - 2011

Rotating a pencil twice about two different points gives surprising results...

Weekly Problem 13 - 2016

The circle of radius 4cm is divided into four congruent parts by arcs of radius 2cm as shown. What is the length of the perimeter of one of the parts, in cm?

Weekly Problem 51 - 2010

Three circles have been drawn at the vertices of this triangle. What is the area of the inner shaded area?

Weekly Problem 11 - 2007

A circle of radius 1 rolls without slipping round the inside of a square of side length 4. Find an expression for the number of revolutions the circle makes.

Weekly Problem 15 - 2008

Which of these graphs could be the graph showing the circumference of a circle in terms of its diameter ?

Weekly Problem 7 - 2014

The diagram shows a shaded shape bounded by circular arcs. What is the difference in area betweeen this and the equilateral triangle shown?

Weekly Problem 23 - 2014

Boris' bicycle has a bigger back wheel than front wheel. Can you work out how many revolutions the back wheel made if the front wheel did 120,000?

Weekly Problem 9 - 2016

The diagram to the right shows a logo made from semi-circular arcs. What fraction of the logo is shaded?

Weekly Problem 30 - 2011

Three touching circles have an interesting area between them...

Weekly Problem 7 - 2006

It takes four gardeners four hours to dig four circular flower beds, each of diameter 4 metres. How long will it take six gardeners to dig six circular flower beds, each of diameter six metres?

Weekly Problem 19 - 2006

What is the total area enclosed by the three semicicles?

Weekly Problem 39 - 2011

Of these five figures, which shaded area is the greatest? The large circle in each figure has the same radius.

Weekly Problem 5 - 2015

The diagram shows four equal discs and a square. What is the perimeter of the figure?

Weekly Problem 4 - 2012

What fraction of the volume of this can is filled with lemonade?

Weekly Problem 31 - 2015

The diagram shows 8 circles surrounding a region. What is the perimeter of the shaded region?

Weekly Problem 4 - 2006

Work out the radius of a roll of adhesive tape.

Weekly Problem 5 - 2006

How many times does the inside disc have to roll around the inside of the ring to return to its initial position?

Weekly Problem 24 - 2008

The diagram shows two circles and four equal semi-circular arcs. The area of the inner shaded circle is 1. What is the area of the outer circle?

Weekly Problem 42 - 2006

Can you work out the shaded area surrounded by these arcs?

Weekly Problem 52 - 2015

Four semicircles are drawn on a line to form a shape. What is the area of this shape?

Weekly Problem 52 - 2014

Four arcs are drawn in a circle to create a shaded area. What fraction of the area of the circle is shaded?

Weekly Problem 51 - 2015

Charlie is making clown hats from a piece of cardboard. What is the maximum number he can make?