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Two circles intersect in the Cartesian Coordinate system at points $A$ and $B$. Point $A$ lies on the line $y=3$. Point $B$ lies on the line $y=12$. These two circles are also tangent to the x-axis at points $P$ and $Q$. How would one find the distance of $AB$ in terms of $PQ$? I managed to prove that $\angle PAQ+\angle PBQ=180$ (edited from before thanks to J.D) but i dont know if that gets anywhere. Thanks!

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    Are you sure that $\angle PAQ=\angle PBQ$? I might be wrong but here is how I picture this problem in my mind [drawing](http://i.stack.imgur.com/bWO6m.png).2012-02-25
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    Im sorry, i mean to say $\angle PAQ + \angle PBQ=180$, so the circles around $PAQ$ and around $PBC$ are congruent. I have edited my post2012-02-25

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