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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

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Rotating Triangle

What happens to the perimeter of triangle ABC as the two smaller circles change size and roll around inside the bigger circle?

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Pericut

Two semicircle sit on the diameter of a semicircle centre O of twice their radius. Lines through O divide the perimeter into two parts. What can you say about the lengths of these two parts?

LOGO Challenge 11 - More on Circles

Stage: 3 and 4 Challenge Level: Challenge Level:1

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.