Problem
1972 AHSME Problem 32
![[asy] real t=pi/12;real u=8*t; real cu=cos(u);real su=sin(u); draw(unitcircle); draw((cos(-t),sin(-t))--(cos(13*t),sin(13*t))); draw((cu,su)--(cu,-su)); label("A",(cos(13*t),sin(13*t)),W); label("B",(cos(-t),sin(-t)),E); label("C",(cu,su),N); label("D",(cu,-su),S); label("E",(cu,sin(-t)),NE); label("2",((cu-1)/2,sin(-t)),N); label("6",((cu+1)/2,sin(-t)),N); label("3",(cu,(sin(-t)-su)/2),E); //Credit to Zimbalono for the diagram[/asy]](/static/aops/70397cee672d74352b46bfc4ca356c3d1cab26a8.png)
Chords AB and CD in the circle above intersect at E and are perpendicular to each other. If segments AE, EB, and ED have measures 2, 3, and 6 respectively, then the length of the diameter of the circle is
\textbf{(A) }4\sqrt{5}\qquad \textbf{(B) }\sqrt{65}\qquad \textbf{(C) }2\sqrt{17}\qquad \textbf{(D) }3\sqrt{7}\qquad \textbf{(E) }6\sqrt{2}
Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.
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