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

Rotating Triangle

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

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:

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.