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  • Early Years Foundation Stage

Square Pair Circles

Age 16 to 18
Challenge Level Yellow starYellow star
  • Problem
  • Getting Started
  • Student Solutions

Investigate the number of points with integer coordinates on circles with centres at the origin for which the square of the radius is a power of 5. 

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Baby Circle

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?

Orthogonal Circle

Given any three non intersecting circles in the plane find another circle or straight line which cuts all three circles orthogonally.

Ellipses

Here is a pattern for you to experiment with using graph drawing software. Find the equations of the graphs in the pattern.

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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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