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# LOGO Challenge 11 - More on Circles

The result of the substitutions 314 and 100 into the two procedures produce the same circles.

This can be confirmed by rearranging the formula: $C=\pi d$.

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Age 11 to 16

Challenge Level

- Problem
- Teachers' Resources

The result of the substitutions 314 and 100 into the two procedures produce the same circles.

This can be confirmed by rearranging the formula: $C=\pi d$.

Experimentation with this relationship through investigating
the two procedures and creating circles which touch and/or which
are related by particular enlargements all support familiarity with
the relationship between the diameter and circumference of any
circle.

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

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?

M is any point on the line AB. Squares of side length AM and MB are constructed and their circumcircles intersect at P (and M). Prove that the lines AD and BE produced pass through P.