I need help proving this problem:
$AB$ is a diameter of a circle. $CD$ is a chord parallel to $AB$ and $2CD = AB$. The tangent at B meets the line $AC$ produced at $E$. Prove that $ AE = 2AB $.
What I've got so far is this:
on extending the line $CD$ to the tangent at $B$ such that $CD$ and the tangent meet at some point $H$, I know that $CH = \dfrac 34 AB$. So from this I know that $CE = \dfrac 3 4 AE.$
How to go further?