I’ve recently come across a puzzle that which I feel like might require more straightforward logic than what I was trying to do (which was trying to find the functions of the two circles inside the bigger quarter circles and then somehow solving r from temporary x and y variable from there)…

Note, there are a few rules that apply to this puzzle here: 1. Two points of the full circle are tangent to two crucial points to solve the puzzle: a point on the left quarter circle with a 1 unit radius as well as the x axis… 2. Two points of the semicircle are tangent to two crucial points to solve the puzzle: a point on the right quarter circle with a 1 unit radius as well as a point tangent to the full circle (1/2r above the x axis)… 3. The x axis splits right down the middle of the semicircle… 4. The available 90 degree points of the quarter circles are tangent to the x and y axes…