An isosceles triangle with base 18 and legs 15 sits in a circle so that each of the edges touches the circumference. Find the radius of the circle.

I think this has something to do with similar triangles (constructing another flipped triangle under the base of the isosceles one), but I can't find the reason why the triangles would be similar. Looks like it has something to do with cyclic quads. Please help, thanks.