I Calculating area of multiple connected circles

1. Jul 17, 2017

magnetics

Hopefully this is a challenging maths problem for someone. This problem is to compare the surface area of the 4 identical circles with the circle overlayed drawn in pencil.

The attached image shows 4 circles, each with diameter x.
To solve the problem, I need to calculate the maximum separation between the circles represented by the circle B with diameter B.

Once B can be calculated, 2x + B will be the diameter of a single circle overlayed over the four as shown in pencil.

This seems to me to be the simplest method to compare the difference in surface area between the four circles and the overlayed circle
i.e. the four circles -> πx2
and the overlayed circle -> π(x+B/2)2

Or there maybe an easier way I have overlooked??

Thank you.

NOTE:
The surface area of the four circles uses the formula πr2, but where r = x/2 and for four identical circles is 4 x π(x/2)2 which is 4πx2/4 which is πx2

Sorry if I'm not very familiar with using the correct symbols on this platform.

Attached Files:

• Quas-Array-Device-Comparrison.jpg
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Last edited: Jul 17, 2017
2. Jul 17, 2017

Staff: Mentor

Make a triangle with the centers of two "S" circles and one "N" circle (or vice versa), and you'll find a method that is much easier than area calculations.

3. Jul 20, 2017

magnetics

Right you are mfb.
Thank you!