Question

$A B$ is a diameter of a circle. $C D$ is a chord parallel to $A B$ and $2 C D=A B$. The tangent at $B$ meets the line $A C$ produced at $E$ and $A E=K \cdot A B$, then $K$ is equal to

Answer 1

$x^{2}+y^{2}=4 a^{2}$
$(-a, a \sqrt{3}) ; \tan \theta=\frac{a \sqrt{3}}{a}=\sqrt{3}$
$ \Rightarrow \theta=60^{\circ}$
$\cos 60^{\circ}=\frac{4 a}{A E}$
$A E=8 a=2 A B$