Two circles have the same centre 
. The smaller circle has a radius of 
cm, while the larger has a radius of 
cm. The circles enclose a region 
, which is subtended by angle of 
at , as shaded.
The area of is 
cm2, where is a constant and 
Let 
cm be the perimeter of
(a) By finding expressions for the area and perimeter of show that 
(b) Show that if the perimeter is minimised, then must be less than 
.
(a)        I like it when the first part requires the student to show something and the second part has them use it (that way they can still do the second part even if they couldn’t do the first part). (b)     Both  and are greater than zero, therefore  and is a minimum.Substitute into the Area formula    Now  Hence  and  |