In ∆MNO, MN = 6 units, MO = 4 units and NO = 12 units. If the bisector of angle M meets NO at P, calculate NP.
A
4.8 units
B
7.2 units
C
8.0 units
D
18.0 units
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
bisector theorem:
\(\frac{|MN|}{|MO|}\) = \(\frac{|PO|}{|NP|}\)
taking the bisected angle:x and y = |ON|=12
: x+y= 12
x = 12 - y
|PO| = 12 - y
\(\frac{6}{4}\)= \(\frac{12-y}{y}\)
6y = 4 (12-y)
6y = 48 - 4y
= 4.8
Recall that x+y= 12
12 - 4.8 =7.2
Source: Myschool Past Questions Archive (Record #28)