Can You Solve This Maths Puzzle From @scientificamerican?

[00:00:00]Four identical semicircles are arranged in a larger outer circle as shown containing a smaller inner circle with area four.

[00:00:09]If each semicircle has an area of 18, what is the area of the outer circle?

[00:00:16]And here's the solution courtesy of Proof Positive, a free weekly math newsletter from Scientific American. Let R, S, and T be the radii of the inner circle, the semicircles, and the outer circle, respectively. Therefore, according to Pythagoras' theorem, T squared must be equal to R plus S squared plus S squared. The area of the inner circle is given by pi R squared, but we know this is equal to four. The area of a semicircle is given by pi S squared divided by two, and this is equal to 18. This means R is equal to two divided by root pi, and S is equal to six divided by root pi. Substituting both of these values into the Pythagorean equation for T squared, we get this is equal to 100 divided by pi.

[00:01:15]Therefore, the outer circle, which has area pi times T squared, is 100. Very well done if you managed to solve that one. If you would like more free puzzles like this in your inbox, then sign up for Proof Positive from Scientific American. Just click the link on screen or head to siam.com/proofpositive.