the solution need some calculations

See the image

The center of arc is on the line AB

C, O and T are aligned

AB and OB are known

The radius of arc is the sum of CO and R

CO is calculated by Pytagore theorem

Finaly we obtain the équation at the bottom of the picture

Solving this équation is easy placing the square root in a side and the rest on the other by sqaring all. We obtain x = 262.5

The radius of the arc is 150 + 262.5

Point C is the center of the arc.