11. Polly has three circles cut from three pieces of coloured card. She originally places them on top of each other as shown. In this configuration the area of the visible black region is seven times the area of the white circle.

Polly moves the circles to a new position, as shown, with each pair of circles touching each other. What is the ratio between the areas of the visible black regions before and after?
A $3: 1$
B $4: 3$
C $6: 5$
D $7: 6$
E 9: 7
SOlUTION
D

The areas of the circles stay the same in the movement, therefore the amount of black covered by the grey circle is the same.
The white circle goes from being on top of the grey to covering part of the black. This will reduce the visible area of the black circle by the area of the white circle. Therefore the area is reduced by one-seventh. Hence the visible area of the black circle becomes six-sevenths of its original value. So the required ratio is $1: \frac{6}{7}=7: 6$.