Question

In triunghiul ABC, M apartine (AB), N apartine (AC), astfel incat AM/MB=2/5 si CN/CA=5/7.Calculati lungimea segmentului MN,daca BC=21 cm.

Answer 1

AM/MB=2/5
CN/CA=5/7  dar AN=CA-CN
facem proportii derivate: CN/(CA-CN)=5/(7-5)⇒CN/AN=5/2⇒AN/CN=2/5
cum si AM/MB=2/5 din reciproca teoremei lui Thales fiindca avem rapoarte egale ne rezulta ca MN II BC
daca MN II BC ⇒ΔAMN asemenea ΔABC⇒AM/AB=MN/BC
AM/MB=2/5⇒AM/(AM+MB)=2/(2+5)⇒AM/AB=2/7
deci 2/7=MN/21⇒MN=21*2/7=6 CM