Line $l$ and line $m$ lie in the same plane but have no points in common. They are both tangent to a circle of area $9$. What is the shortest distance between any point on $l$ and any point on $m$?

Since the parallel lines have no points in common, the circle lies between them, meaning the shortest distance between the lines equals the diameter of the circle. The area of the circle is given as 9, and using the area formula pi times radius squared equals 9 gives a radius of 3. The diameter is twice the radius, so the shortest distance between any point on line l and any point on line m is 6.

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