Hello, immunofort!

Chris is absolutely correct . . . and he *did* give you a nudge, right? Code:

A *
** * 2
* * *
x * * * D
* * *
* * *
B * * * *
1 C

Use Pythagorus in $\displaystyle \Delta ABC$

$\displaystyle AC^2 \:=\:AB^2 + BC^2\quad\Rightarrow\quad AC^2 \:=\:x^2+1\quad\Rightarrow\quad AC \:=\:\sqrt{x^2+1}$

Use Pythagorus in $\displaystyle \Delta ADC$

$\displaystyle CD^2 + AD^2 \:=\:AC^2\quad\Rightarrow\quad CD^2 + 2^2 \:=\:(\sqrt{x^2+1})^2 \quad\Rightarrow\quad CD^2 + 4 \:=\:x^2+1$

Therefore: .$\displaystyle CD^2 \:=\:x^2-3 \quad\Rightarrow\quad CD \:=\:\sqrt{x^2-3} $