Sixteen unit circles are placed together as shown in the diagram.
Find the radius of the shaded circle in the centre.
We begin be drawing a large square and a quarter square on the diagram.
Let us consider the top right quadrant.
Using the Pythagorean Theorem, 22 = a2 + a2 a = 2.
Similarly, 22 = b2 + 12 b = 3.
As r + 2 = 2 + 3, we get r = 2 + 3 – 2.
If the centres of the circles in the outside ring of the original diagram are joined, will it form a regular dodecagon?