Regular polygons and circles

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

Part the Polygons

Age

7 to 11

Challenge level

Draw three straight lines to separate these shapes into four groups - each group must contain one of each shape.
problem

Circle Panes

Age

7 to 11

Challenge level

Look at the mathematics that is all around us - this circular window is a wonderful example.
problem

Sports Equipment

Age

7 to 11

Challenge level

If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?
problem

Circular Area

Age

7 to 11

Challenge level

How could you find out the area of a circle? Take a look at these ways.
problem

Hexagon Transformations

Age

7 to 11

Challenge level

Can you cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!