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Fixing It

A and B are two fixed points on a circle and RS is a variable diamater. What is the locus of the intersection P of AR and BS?

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Pericut

Two semicircle sit on the diameter of a semicircle centre O of twice their radius. Lines through O divide the perimeter into two parts. What can you say about the lengths of these two parts?

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Set Square

A triangle PQR, right angled at P, slides on a horizontal floor with Q and R in contact with perpendicular walls. What is the locus of P?

Virtual Geoboard


There are many activities that make use of a pinboard or geoboard. By using the controls at the bottom of the interactivity you can change the number of points around the circle - or select a geoboard with a central pin - or create a square pinboard.
Click on the colour bands, then drag the band you create onto the board. To attach them you will need to pull them over the pegs. To change their position - or remove them - "loop" them off each peg in turn.

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If you would like to work on paper, the Printable Resources page has links to printable sheets of circles with a range of numbers of circumferential dots.
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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NRICH is part of the family of activities in the Millennium Mathematics Project.