If you have no idea on what to spend $500 on, you don't need to spend it on anything.
Bank it, wait until you need something that you can buy with $500.
The large semicircle must have its corners touching two adjacent edges of the square, and its arc must also touch two adjacent edges of the square. There's only one way to acheive this (that I can see.) The smaller one fits snugly in the remaining gap. Sorry for not making it clear.
Well done :) now for a more difficult one.
The diagram shows two semicircles inside a square of side length 1. The common centre of both semicircles lies on a diagonal of the square.
What is the shaded area?
I use F R U R' U' F' for the line and R' U' F' U F R for the L, because I didn't like the sound of double layer turns. For dot, either one after the other.
Nice and simple two-look OLL algs.