1992 AHSME Problem 30

Let ABCD be an isosceles trapezoid with bases AB=92 and CD=19. Suppose AD=BC=x and a circle with center on \overline{AB} is tangent to segments \overline{AD} and \overline{BC}. If m is the smallest possible value of x, then m^2=

\text{(A) } 1369\quad \text{(B) } 1679\quad \text{(C) } 1748\quad \text{(D) } 2109\quad \text{(E) } 8825

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