Tangent Curve between existing circle and line

I Need some help constructing the below shape...

i have no issue creating the 2 tangent curves from the end of each of the straight lines

However, how do you then get the 2 curves to them meet at their tangent also?

Modify - Fillet  (with Trim, and radius set at the Tool Options bar).

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.