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Roaming Rhombus

Age 14 to 16
Challenge Level Yellow star
Secondary curriculum
  • Problem
  • Student Solutions

Well done Luke and Daniel from year 9 together with Nicholas and Luke from year 7 of Clevedon Community School who sent in the following solution.

The locus of corner D will be a circle with a radius equal to AD, whose centre is A. The locus of the point Y will be a circle with a radius equal to AD, and a centre on AB one third of the way along from A to B.

Can you see the reason for this? The locus of Y is a circle. If you imagine a line joining Y to the centre Z of this circle then DYZA is a parallelogram so ZY = AD and AZ=DY.


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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.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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