Two chords $AB$ and $AC$ are drawn inside a circle with diameter $AD$. The angle $BAC = 60$, $AB = 24cm$, $EC = 3cm$, and $BE$ and $AC$ are perpendicular. What is the length of the chord $BD$?
Here's what I've tried:
$ABE = 30$ which implies $AE = 12cm$ and therefore $BE = 12\sqrt3cm$ and $BC = 21cm$. Call the intersection of $EB$ and $AD$ point $O$. So we have $AEO$ is similar to $ACD$ but I don't know where to go from here.
Thank you so much in advance!