The triangle ABC with an angle of C 30 degrees at the vertex C is inscribed in a circle with a center O and a radius of 9 cm. If R is the radius of the circle tangent to the segments AO and BO, and the arc AB, then R is:?
This is fairly difficult.
Obviously, the circumcenter is $O$ so the perpendicular bisectors are near.
I used: $x = 9\sin(60)$ as an approximate, but it does not work.