### Mean Geometrically

A and B are two points on a circle centre O. Tangents at A and B cut at C. CO cuts the circle at D. What is the relationship between areas of ADBO, ABO and ACBO?

### Just Rolling Round

P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?

### Giant Holly Leaf

Find the perimeter and area of a holly leaf that will not lie flat (it has negative curvature with 'circles' having circumference greater than 2πr).

# Pericut

##### Stage: 4 and 5 Challenge Level:

The figure is made up of three semicircles. The line through $O$ divides the perimeter of this figure into two parts.

What can you say about the lengths of these two parts as you move the points $P$ and $O$?

Created with GeoGebra

NOTES AND BACKGROUND

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