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The circles x^2 + y^2 + 2ax-c^2 = 0 and ...

The circles `x^2 + y^2 + 2ax-c^2 = 0` and `x^2 + y^2 + 2bx-c^2=0` intersect at A and B. A line through A meets one circle at P and a parallel line through B meets the other circle at Q. Show that the locus of the mid-point of PQ is a circle.

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