Weekly Problem 37 - 2014

Which of the five diagrams below could be drawn without taking the pen off the page and without drawing along a line already drawn?

Weekly Problem 13 - 2012

The diagram shows contains some equal lengths. Can you work out one of the angles?

Can you find the radius of the circle inscribed inside a '3-4-5 triangle'?

Weekly Problem 23 - 2008

A triangle has been drawn inside this circle. Can you find the length of the chord it forms?

Two semicircles overlap, can you find this length?

Can you find the ratio of the area shaded in this regular octagon to the unshaded area?

Weekly Problem 12 - 2016

The diagram shows a square PQRS and two equilateral triangles RSU and PST. PQ has length 1. What is the length of TU?

Weekly Problem 41 - 2016

The diagram shows a square, with lines drawn from its centre. What is the shaded area?

Weekly Problem 29 - 2010

An isosceles triangle is drawn inside another triangle. Can you work out the length of its base?

Weekly Problem 21 - 2012

Two rectangles are drawn in a rectangle. What fraction of the rectangle is shaded?

Weekly Problem 43 - 2017

The diagram shows a semicircle inscribed in a right angled triangle. What is the radius of the semicircle?

Weekly Problem 1 - 2011

Use facts about the angle bisectors of this triangle to work out another internal angle.

Weekly Problem 4 - 2008

In the figure given in the problem, calculate the length of an edge.

Weekly Problem 27 - 2014

Four congruent isosceles trapezia are placed in a square. What fraction of the square is shaded?

Weekly Problem 34 - 2008

What is the area of the region common to this triangle and square?

Weekly Problem 15 - 2015

In the diagram, two lines have been drawn in a square. What is the ratio of the areas marked?

Weekly Problem 44 - 2009

A garden has the shape of a right-angled triangle. A fence goes from the corner with the right-angle to a point on the opposite side. How long is the fence?

A semicircle is drawn inside a right-angled triangle. Find the distance marked on the diagram.

Weekly Problem 8 - 2010

Are you able to find triangles such that these five statements are true?

This square piece of paper has been folded and creased. Where does the crease meet the side AD?

Can you find the area of the triangle from its height and two sides?

In the diagram, the radius of the circle is equal to the length AB. Can you find the size of angle ACB?

Just from the diagram, can you work out the radius of the smaller circles?