Weekly Problem 33 - 2017

If the midpoints of the sides of a right angled triangle are joined, what is the perimeter of this new triangle?

Weekly Problem 23 - 2007

If two of the sides of a right-angled triangle are 5cm and 6cm long, how many possibilities are there for the length of the third side?

Weekly Problem 40 - 2009

This quadrilateral has an unusual shape. Are you able to find its area?

Weekly Problem 48 - 2007

A 3x8 rectangle is cut into two pieces... then rearranged to form a right-angled triangle. What is the perimeter of the triangle formed?

Weekly Problem 10 - 2010

Can you calculate the length of this diagonal line?

Can you work out the area of this isosceles right angled triangle?

Weekly Problem 3 - 2012

Find out how many pieces of hardboard of differing sizes can fit through a rectangular window.

Weekly Problem 21 - 2014

A parallelogram is formed by joining together four equilateral triangles. What is the length of the longest diagonal?

Weekly Problem 11 - 2012

A rectangular piece of paper is folded. Can you work out one of the lengths in the diagram?

How does the perimeter change when we fold this isosceles triangle in half?

Weekly Problem 20 - 2011

What is the perimeter of this unusually shaped polygon...

The top square has been rotated so that the squares meet at a 60$^\text{o}$ angle. What is the area of the overlap?

A vine is growing up a pole. Can you find its length?

Weekly Problem 33 - 2007

Two circles touch, what is the length of the line that is a tangent to both circles?

Weekly Problem 5 - 2013

The diagram shows 8 shaded squares inside a circle. What is the shaded area?

A palm tree has snapped in a storm. What is the height of the piece that is still standing?

Can you work out the radius of a circle from some information about a chord?

Can you find the length of the third side of this triangle?

Weekly Problem 14 - 2014

Triangle T has sides of lengths 6, 5 and 5. Triangle U has sides of lengths 8, 5 and 5. What is the ratio of their areas?

A square has area 72 cm$^2$. Find the length of its diagonal.

Weekly Problem 2 - 2008

The diagram shows two semicircular arcs... What is the diameter of the shaded region?

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?

Work your way through these right-angled triangles to find $x$.

Weekly Problem 5 - 2008

Calculate the ratio of areas of these squares which are inscribed inside a semi-circle and a circle.

Weekly Problem 3 - 2011

What does Pythagoras' Theorem tell you about the radius of these circles?

Weekly Problem 22 - 2006

A rectangular plank fits neatly inside a square frame when placed diagonally. What is the length of the plank?

Two arcs are drawn in a right-angled triangle as shown. What is the length $r$?

Can you find the distance from the well to the fourth corner, given the distance from the well to the first three corners?

Two ribbons are laid over each other so that they cross. Can you find the area of the overlap?

Can you find the perimeter of the pentagon formed when this rectangle of paper is folded?

Weekly Problem 43 - 2009

This diagram has symmetry of order four. Can you use different geometric properties to find a particular length?

How much of the inside of this triangular prism can Clare paint using a cylindrical roller?

When you pull a boat in using a rope, does the boat move more quickly, more slowly, or at the same speed as you?

Weekly Problem 16 - 2014

The diagrams show squares placed inside semicircles. What is the ratio of the shaded areas?

Can you find the radius of the larger circle in the diagram?

Can you work out the length of the diagonal of the cuboid?

How do these measurements enable you to find the height of this tower?

A circle of radius 1 is inscribed in a regular hexagon. What is the perimeter of the hexagon?

Can you find all the integer coordinates on a sphere of radius 3?

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 49 - 2015

A window frame in Salt's Mill consists of two equal semicircles and a circle inside a large semicircle. What is the radius of the circle?

Can you find the length and width of the screen of this smartphone in inches?

Weekly Problem 28 - 2008

The diagram shows a semi-circle and an isosceles triangle which have equal areas. What is the value of tan x?