Given an arc PQ with curvature 1/9, Three identical circles with radii 3 and centered at B,G,A respectively. The circumference of the circles pass through each other's centers. Find the area of the shaded region.
I actually got the results already. I was wondering if there is an alternative solution. I wanted to see if this can be solved using polar integration by letting G be the origin. The area of the black circle can be solved using polar integration by getting angle CGE. Which can be derived by cosine law. I was wondering if it is also possible for the blue area by getting angle DGF? But I couldn't seem to get it anymore by using cosine rule.
Also is there an alternative solution to solve the red area other than 2(sector GBH - triangle GBH)?