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VS 2010 Intersecting lines

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Been a while since I have written any code and I am attempting to write an app for general public use, whereby I start with a small drawn circle and keep enlarging it until it hits a boundary line of another irregular shape that surrounds it. The purpose is to determine the closest point of the surrounding shape to the centre of the circle.

So what I need to do is work out is how to tell when the increasing circle touches a line or point of surrounding shape. I can easily tell the distance from that point back to the centre by calculating the radius of the circle just not sure how to determine the contact point. For simplicity purposes if we call the outer shape a rectangle and place the small circle in any spot that is not central.

Appreciate any pointer or code you might be able to provide.

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