Hi,
You don't need to solve any Pythagoras:
0.- Put the origin at "O"
1.- Get the slope of each tangent line, say m1, m2
2.- The slope of the radius line for each tangent will be -1/m1; -1/m2, so you get the angles Delta1 y Delta2
3.- The point "t" will be at (0, R2)
4.- The point T2 will be at (R2*cos(Delta2),R2*Sin(Delta2))
5.- The same for T1 (need some sign change)
6.- Translate the result to real origin
Gaston Nunez