...it will be difficult in illustrator as you need to know two things, the size of the circle (it's centre point/radius) and how far the intersection point needs to be on the left side 50 degree angle path...

...my thoughts are:

...assuming that the circles top/middle anchor point sits on the top/right anchor of the 50 degree shape, the intersection on the left hand side of the 50 degree shape is governed by the size of the circle...

...the centre point of that circle falls somewhere down the y axis of the top right anchor point of the 50 degree shape, that is the unknown point that needs to be calculated...

...from the circles centre point, the 50 degree point is where the intersection occurs on the shape...

...attached is a diagram to explain my thoughts on a known shape and it's dimensions...

http://www.zen63258.zen.co.uk/tek/Screen%20shot%202009-12-31%20at%2013.37.48.png

...there probably is a formula for working it out, but i am yet to find what that might be, math not my strongest area, it is possible a dedicated CAD program can assist with this if you require "absolute" perfection...

...in illustrator though, it can often be a case of zooming in to max and view in outline mode, that will get you near enough...




 

andrew

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  www.apepp.info
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...when you have the circle at the point of intersection, the pathfinder command to use is "divide" or "trim", you can then remove the bits you don't want, then with the remaining parts, use the "unite" or  "merge" function...

 

andrew

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  www.apepp.info
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Thank you for the response, i think this is probably something i would need. I will try to figure it out, if you come up with any solutions please let me know. Once again, thank you.