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?

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.

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

Weekly Problem 27 - 2014

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

Weekly Problem 23 - 2008

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

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 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?

Weekly Problem 8 - 2010

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