2007 AMC 12B Problem 14

Point P is inside equilateral \triangle ABC. Points Q, R, and S are the feet of the perpendiculars from P to \overline{AB}, \overline{BC}, and \overline{CA}, respectively. Given that PQ=1, PR=2, and PS=3, what is AB?

\mathrm {(A)} 4\qquad \mathrm {(B)} 3\sqrt{3}\qquad \mathrm {(C)} 6\qquad \mathrm {(D)} 4\sqrt{3}\qquad \mathrm {(E)} 9

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.