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Age 14 to 16
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  • ABCD is a square.
  • P is the midpoint of AB and is joined to C.
  • A line from D perpendicular to PC meets the line at the point Q.
Prove AQ = AD.

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Polycircles

Show that for any triangle it is always possible to construct 3 touching circles with centres at the vertices. Is it possible to construct touching circles centred at the vertices of any polygon?

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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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