Question

Triunghi ABC,M apartine AB,MN ll BC,N apartine AC
a)AM=3,MN=6,AB=10,AN=5,aflati MB,AN,NC
b)MN=5,BC=15,AC=12,AB=9,aflati AM,MB,AN,NC
c)MN=1,BC=4,NC=2,AM=8,aflati AB,AC,AN,MB

Answer 1

ΔABC,M apartine AB,MN ll BC,N apartine AC⇒ΔAMNasemeniΔABC⇒AM/AB=AN/AC=MN/BC
A-
MB=AB-AM=10-3=7
AM/AB=AN/AC⇒3/10=5/AC⇒AC=50/3=16,(6)

NC=AC-AN=16,(6)-3=13,(6)

B-
AM/AB=AN/AC=MN/BC⇒AM/9=AN/12=5/15⇒AM/9=5/15⇒AM=3
AN/12=5/15⇒AN=4

MB=AB-AM=9-3=6
NC=AC-AN=12-4=8


C-
AM/AB=AN/AC=MN/BC⇒8/AB=AN/AC=1/4⇒8/AB=1/4⇒AB=8*4=32

MB=AB-AM=32-8=24

AN/AC=1/4⇒AC-NC/AC=1/4⇒AC-2/AC=1/4⇒4(AC-2)=AC⇒4AC-8=AC⇒3AC=8⇒AC=8/3=2,(6)

AN=AC-NC=2,(6)-2=0,(6)