# Менелайн теорем

## Менелайн теорем

$\dpi{100}&space;ABC$ гурвлжны $\dpi{100}&space;AB,&space;BC,&space;CA$ талууд ба тэдгээрийн үргэлжлэл дээр харгалзан $\dpi{100}&space;C_{1},A_{1},B_{1}$ цэгүүд нэг шулуун дээр оршиж байх зайлшгүй бөгөөд хүрэлцээтэй нөхцөл $\dpi{100}&space;\frac{\left&space;|AB_{1}&space;\right&space;|}{\left&space;|B_{1}C&space;\right&space;|}\cdot\frac{\left&space;|CA_{1}&space;\right&space;|}{\left&space;|A_{1}B&space;\right&space;|}\cdot&space;\frac{\left&space;|BC_{1}&space;\right&space;|}{\left&space;|C_{1}A&space;\right&space;|}=1$ байх явдал юм.  Баталгаа.  Зураг-1.   $\dpi{100}&space;\frac{\left&space;|AB_{1}&space;\right&space;|}{\left&space;|B_{1}C&space;\right&space;|}=\frac{m}{n}&space;(1)$ Зураг-2.  $\dpi{100}&space;\frac{\left&space;|CA_{1}&space;\right&space;|}{\left&space;|A_{1}B&space;\right&space;|}=\frac{n}{l}&space;(2)$ Зураг-3.  $\dpi{100}&space;\frac{\left&space;|BC_{1}&space;\right&space;|}{\left&space;|C_{1}A&space;\right&space;|}=\frac{l}{m}&space;(3)$ харьцаа  $\dpi{100}&space;(1),(2),(3)$  ëсоор  $\dpi{100}&space;\frac{\left&space;|AB_{1}&space;\right&space;|}{\left&space;|B_{1}C&space;\right&space;|}\cdot\frac{\left&space;|CA_{1}&space;\right&space;|}{\left&space;|A_{1}B&space;\right&space;|}\cdot&space;\frac{\left&space;|BC_{1}&space;\right&space;|}{\left&space;|C_{1}A&space;\right&space;|}=\frac{m}{m}\cdot&space;\frac{n}{l}\cdot&space;\frac{l}{m}=1$ болж теорем батлагдав.