DataPakP

My known/controlled variables thus far are the coordinates of C and T, the length of line CT (aka the radius of circle C), the angle A (in degrees) and thus the angle of the tangent line which I believe would be the reciprocal of angle A.

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Now specifically, I'm trying to figure out how I can use the given information combined with a desired length L away from the tangential point in either direction to find the XY coordinates of this new point (represented in bright green). I'm able to calculate the XY of the tangent point T (given point C, the radius of C aka line CT, and my chosen angle A) but beyond that I'm lost.

[This is the best representation I can think of o