In the adjoining figure, pint Q is on the side MP such that MQ = 2 and MP = 5.5. Ray NQ is the bisector of ∠ MNP of ∆ MNP. Find MN:NP.

Solution :

M, Q and P are collinear points

∴ MP  = MQ + QP   [∵ M – Q – P ]

∴ 5.5 = 2 + QP

∴ 5.5 – 2 = QP

∴ QP = 3.5

In ∆MNP , Ray NQ is the bisector of ∠MNP of ∆ MNP,

MN = MQ [By Angle bisector theorem] NP QP

MN = 2 NP 3.5

MN = 2 × 10 NP 3.5 × 10

MN = 20 NP 35

MN = 4 NP 7

∴ MN : NP = 4: 7