Let $AB$ and $CD$ be perpendicular strings in the circle $\Gamma$.
$E$ is their point of intersection.
It is given that:
$1) AB=11$
$2) DE=6$
$3)$ The distnace between the string $CD$ and the circle center is $3.5$.
Here is a drawing:
I need to find $CD$ and calculate the distance between $AB$ and the circle center.
My attempt -
I said that $BE=x$, then $AE=11-x$ and I used the fact that:
If in a circle two strings are cut, then the product of one string segment equals the product of the other string segments, to get $CE=\frac{AE\boldsymbol{\cdot} BE}{ED}=\frac{x(11-x)}{6}$
From here, by Pythagoras theorem, I got that :
$AD=(11-x)^2+36$, and $BC=x^2+(\frac{x(11-x)}{6})^2=x^2(1+\frac{(11-x)^2}{6})$.
That's that. Can't think of anything else.
One more thing is that I'm not allowed to use trigonometry. I.e $\sin(x), \cos(x)$, and so forth.
Please help!