MN=6cm
NP= 4 cm
Step-by-step explanation:
Step 1:
By the property of symmetry in triangle
[tex]\frac{BA}{BC} =\frac{MN}{NP}[/tex]
By applying componendo and dividendo rule above equation is modified as
[tex]\frac{BA+BC}{BA-BC} = \frac{MN+NP}{MN-NP}[/tex]
Step 2:
Applying the values in above equation
[tex]\frac{12+8}{12-8} =\frac{10}{MN-NP}[/tex]
on simplification
MN-NP= [tex]\frac{10*4}{20}[/tex]
MN-NP=2
MN+NP=10
on solving above equations
2[tex]*[/tex]MN=12
MN=6 cm
NP=10-MN
=10-6
=4 cm
