Z podobieństwa trójkątów MCD i MBA:

$\frac{\left|CM\right|}{\left|CD\right|}=\frac{\left|BM\right|}{\left|AB\right|}$  

$\frac{\left|CM\right|}{\left|CD\right|}=\frac{\left|CM\right|+\left|BC\right|}{\left|AB\right|}$  

 

Skorzystajmy z założenia:

$\frac{\left|AB\right|}{\left|CD\right|}=\frac{7}{5}$

$\left|AB\right|=\frac{7}{5}\left|CD\right|$   

a więc:

$\frac{\left|CM\right|}{\left|CD\right|}=\frac{\left|CM\right|+\left|BC\right|}{\left|\frac{7}{5}\right|CD\mid }\left|:\right|CD\mid$  

$\left|CM\right|=\frac{5}{7}\left(\left|CM\right|+22\right)$  

$\left|CM\right|=\frac{5}{7}\left|CM\right|+\frac{110}{7}$  

$\frac{2}{7}\left|CM\right|=\frac{110}{7}\mid \cdot 7$  

$2\left|CM\right|=110$  

$\left|CM\right|=55\left[\text{cm}\right]$