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
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?
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).
This problem attracted several correct
answers anonymously submitted by students at Madras College
. This solution is included because of its