help with geometry

There is some simple circle geometry formula for this.

I am pretty sure I have seen Heureka use it.

help with geometry

$\begin{array}{|rcll|} \hline \mathbf{ \overline{NM}*\overline{AM} } &=& \mathbf{ \overline{LM}*\overline{KM} } \\ (x-4)*(3+x-4) &=& (x-5)*(6+x-5) \\ (x-4)*(x-1) &=& (x-5)*(x+1) \\ x^2-x-4x+4 &=& x^2+x-5x-5 \\ -x-4x+4 &=& +x-5x-5 \\ -5x+4 &=& -4x-5 \\ -x &=& -9 \\ \mathbf{x} &=& \mathbf{9} \\ \hline \end{array}$

$\begin{array}{|rcll|} \hline \mathbf{\overline{KM}} &=& \mathbf{6+x-5} \\ \overline{KM} &=& x+1 \quad | \quad \mathbf{x=9} \\ \overline{KM} &=& 9+1 \\ \mathbf{\overline{KM}} &=& \mathbf{10} \\ \hline \end{array}$