MHB Axis Constrained Collision Distance

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I have 2 curves and I need to slide 1 of the circles along an axis until it exactly meets the other circle. How do I determine the distance until contact?
 

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Draw a line from the center of the larger circle in the direction of its travel. You need to know the perpendicular-line distance from the center of the smaller circle to the drawn line. It is impossible to solve the problem without some information along those lines.
 

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