Split isosceles down the middle into two right angled triangles.

Each with base 9 and hypotenuse 15

Angle opposite base is arcsin (9/15) = arcsin (3/5)

So angle at top of isosceles is 2 arcsin (3/5)

Join the centre of the circle to the two ends of the base forming a second isosceles triangle

By circle theorems angle at top of second isosceles triangle is twice that at top of first isosceles triangle (4 arcsin (3/5))

Split second isosceles triangle into two right angled triangles as we did with the first one

Each with base 9, no other side known and angle at top half of 4 arcsin (3/5)

ie 2 arcsin (3/5), call this A and radius r

Then sin A = r/9

r = 9 sin A = 9 sin (2 arcsin (3/5))