There is a circle with centre at the origin of radius 1. In this problem, we want designs where circles touch adjacent circles but do not intersect them a second time.
a) How many circles of radius 1 could fit around the centre circle, so that the outer circles touch two adjacent outer circles and the centre circle?
b) What is the radius of the outer circles if you can fit four of them around the centre circle, so that they touch their adjacent circles and the centre circle once?
c) What is the radius of the smallest amount of circles that still fit this pattern?