In the figure shown, points $A$, $B$, $C$, and $E$ lie on the circle,…

Question

Prompt

In the figure shown, points

A

B

C

, and

E

lie on the circle, and

A B < B C

. Segment

A C

is perpendicular to segment

B E

at point

D

, and

B D = 286

. The diameter of the circle is

145

\frac{C D}{A D} = r

, what is the value of

r