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?

Find the exact values of some trig. ratios from this rectangle in which a cyclic quadrilateral cuts off four right angled triangles.

The absurdity of it!

Find the exact values of $$\sqrt{2 + \sqrt 3}- \sqrt{2 - \sqrt3}$$ and of $$\root 3 \of {2 + \sqrt 5}+ \root 3 \of {2 - \sqrt 5}$$

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.

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

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