- #1

Zekes

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Say I have two identical circles, both of radii of one, overlapping, as shown in the diagram below:

View attachment 9059

In this diagram, x is the circumference of the circles, and the bit of the bottom circle which is drawn blue (the overlapping bit) is 1/6th of the whole circumference.

What I'm looking for is y, which is this:

View attachment 9060

Now, working out x is easy - it's 2 \pi r, thus the overlapping bit is 1/3 \pi r. But how do I proceed in finding y from here? Help is much appreciated! Thanks!

View attachment 9059

In this diagram, x is the circumference of the circles, and the bit of the bottom circle which is drawn blue (the overlapping bit) is 1/6th of the whole circumference.

What I'm looking for is y, which is this:

View attachment 9060

Now, working out x is easy - it's 2 \pi r, thus the overlapping bit is 1/3 \pi r. But how do I proceed in finding y from here? Help is much appreciated! Thanks!