Circle n arc [S]

Say, we have a circle of radius 'a'. Now, draw an arc of a circle of radius 'b' such that its centre lies on the circumference of the first circle, and the end points of the arc are on the circumference as well, as shown below.Here comes the question: What is the ratio of b/a, such that, the area of the blue region is equal to that of the red region.


I wrote a python program and found out that the ratio is constant (=1.159). But, i could not figure out a proper theoretical proof. Im hoping that someone will do it in the comments box.


P.S: A special thanks for Sushama for asking me this cute problem, which fortunately or unfortunately, she doesnt have an answer to.[S]