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Solve bug?

Solve seems to be returning an invalid answer when I do this:

c1 = (-50 + x)^2 + (-50 + y)^2 == 156.25
c2 = (-4.5 + x)^2 + (-56.25 + y)^2 == 156.25

{{x -> 16, y -> 43.75}, {x -> 84, y -> 43.75}}

This answer is so wrong!!??
Those two points are completely off. Not even close.

c1 and c2 are the equations of two overlapping circles.
Use ImplicitPlot to verify this fact.
Why can't Mathematica resolve this simple sytem of equations correctly?

If I am doing something wrong please tell me what it is.

Also how can I cut and paste text from a mathematica notebook without
getting all the slashes?
Your help is greatly appreciated.


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