To find NB in terms of c, we can use the concept of midpoint theorem.
According to the midpoint theorem, in a triangle, if a line segment connects the midpoints of two sides of the triangle, then the length of that line segment is half the length of the third side.
Given that M is the midpoint of AB and N is the midpoint of CM, we can write:
AM = MB / 2
AN = NC / 2
Also, we know that CP = 3a and PA = 6a, so:
AC = AP + PC = 6a + 3a = 9a
Now, using the fact that AM + AN = AN, we have:
MB / 2 + NC / 2 = NB
Substitute the values of MB and NC:
2b / 2 + 9a / 2 = NB
Simplify:
b + 4.5a = NB
So, NB = b + 4.5a
Now, we need to express a in terms of c. Since CP = 3a, we can solve for a:
3a = c
a = c / 3
Now, substitute the value of a back into NB:
NB = b + 4.5(c / 3)
Simplify:
NB = b + 1.5c
So, NB in terms of c is given by NB = b + 1.5c.