Regular polygons and circles

problem
Roll on

Age

14 to 16

Challenge level

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?
problem
Gold yet again

Age

16 to 18

Challenge level

Nick Lord says "This problem encapsulates for me the best features of the NRICH collection."
problem
Semicircle in a semicircle

Age

14 to 16

Challenge level

The diagram shows two semicircular arcs... What is the diameter of the shaded region?
problem
Oh so circular

Age

14 to 16

Challenge level

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?
problem
Circle time

Age

14 to 16

Challenge level

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

Age

11 to 16

Challenge level

Eight lines are drawn in a regular octagon to form a pattern. What fraction of the octagon is shaded?
problem
What shape and colour?

Age

5 to 7

Challenge level

Can you fill in the empty boxes in the grid with the right shape and colour?
problem
2 rings

Age

5 to 7

Challenge level

The red ring is inside the blue ring in this picture. Can you rearrange the rings in different ways? Perhaps you can overlap them or put one outside another?
problem
Olympic rings

Age

5 to 7

Challenge level

Can you design your own version of the Olympic rings, using interlocking squares instead of circles?
problem
Shaping it

Age

5 to 11

Challenge level

These pictures were made by starting with a square, finding the half-way point on each side and joining those points up. You could investigate your own starting shape.