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Math·Geometry and Trigonometry·Circles

hard

In the figure shown, points $A$, $B$, $C$, and $E$ lie on the circle, and $AB<BC$. Segment $AC$ is perpendicular to segment $BE$ at point $D$, and $BD=\sqrt{286}$. The diameter of the circle is $145$. $\frac{CD}{AD}=r$, what is the value of $r$?

1

71.5