Sun of Reuleaux
A Reuleaux triangle is defined in the following way:
- The 3 apex points A, B, and C are one unit from one another
- Each pair of apex points are connected by the arc of a circle of radius 1 whose center is the third apex
- We end up with the yellow region as shown above
What is the radius of the Reuleaux triangle's circumcircle as defined by apex points A, B, and C?
Give your answer to 5 decimal places.