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Incircles explained
This article is about triangles in which the lengths of the sides and the radii of the inscribed circles are all whole numbers.
Regular polygons and circles
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articleArclets explained
This article gives an wonderful insight into students working on the Arclets problem that first appeared in the Sept 2002 edition of the NRICH website. -
articlePi, a very special number
Read all about the number pi and the mathematicians who have tried to find out its value as accurately as possible. -
articleCircles, circles everywhere
This article for pupils gives some examples of how circles have featured in people's lives for centuries. -
articleUsing GeoGebra
Never used GeoGebra before? This article for complete beginners will help you to get started with this free dynamic geometry software.
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problemBaby circle
Age16 to 18Challenge level
A small circle fits between two touching circles so that all three circles touch each other and have a common tangent? What is the exact radius of the smallest circle? -
problemArea i'n it
Age16 to 18Challenge level
Triangle ABC has altitudes h1, h2 and h3. The radius of the inscribed circle is r, while the radii of the escribed circles are r1, r2 and r3 respectively. Prove: 1/r = 1/h1 + 1/h2 + 1/h3 = 1/r1 + 1/r2 + 1/r3 . -
problem2D-3D
Age16 to 18Challenge level
Two circles of equal size intersect and the centre of each circle is on the circumference of the other. What is the area of the intersection? Now imagine that the diagram represents two spheres of equal volume with the centre of each sphere on the surface of the other. What is the volume of intersection?
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problemSangaku
Age16 to 18Challenge level
The square ABCD is split into three triangles by the lines BP and CP. Find the radii of the three inscribed circles to these triangles as P moves on AD. -
problemFitting in
Age14 to 16Challenge level
The largest square which fits into a circle is ABCD and EFGH is a square with G and H on the line CD and E and F on the circumference of the circle. Show that AB = 5EF. Similarly the largest equilateral triangle which fits into a circle is LMN and PQR is an equilateral triangle with P and Q on the line LM and R on the circumference of the circle. Show that LM = 3PQ