Problem
1988 AHSME Problem 27
In the figure, AB \perp BC, BC \perp CD, and BC is tangent to the circle with center O and diameter AD. In which one of the following cases is the area of ABCD an integer?
![[asy] defaultpen(fontsize(10pt)+linewidth(.8pt)); pair O=origin, A=(-1/sqrt(2),1/sqrt(2)), B=(-1/sqrt(2),-1), C=(1/sqrt(2),-1), D=(1/sqrt(2),-1/sqrt(2)); draw(unitcircle); dot(O); draw(A--B--C--D--A); label("$A$",A,dir(A)); label("$B$",B,dir(B)); label("$C$",C,dir(C)); label("$D$",D,dir(D)); label("$O$",O,N); [/asy]](/static/aops/d8d58321572892427739e31ba1afdfbaaf71f9de.png)
\begin{array}{l} \textbf{(A)}\ AB=3, CD=1\qquad \textbf{(B)}\ AB=5, CD=2\qquad \textbf{(C)}\ AB=7, CD=3\qquad\\ \textbf{(D)}\ AB=9, CD=4\qquad \textbf{(E)}\ AB=11, CD=5 \end{array}
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