If you know the angle between the x-axis and this box shaped object you can use some basic trig.
Lets assume the box shaped object has a length of "len". ( It would really help to better label what is going on, I don't fully understand.) and lets say you have an angle of θ.
I'm assuming the centre of the circle has coordinates (0,0).
The then the vertical distance from the centre of the circle to the edge of the circle where the box touches is y = len * sin(θ) and for the horizontal distance is len * cos(θ).
If you are only going about 2/5ths of the way up the box thing you would use len / 5 instead of len.
This is just the math behind it. In c# you want to use the Math class. it has all the functions you need. Be careful with radians and degrees.