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Some(?) of the Parts

A circle touches the lines OA, OB and AB where OA and OB are perpendicular. Show that the diameter of the circle is equal to the perimeter of the triangle

Triangle Incircle Iteration

Keep constructing triangles in the incircle of the previous triangle. What happens?

Medallions

Three circular medallions fit in a rectangular box. Can you find the radius of the largest one?

Circle Scaling

Age 14 to 16
Challenge Level

Circle being scaled

You are given a circle with centre O. Describe how to construct with a straight edge and a pair of compasses, two other circles centre O so that the three circles have areas in the ratio 1:2:3.

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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