Q11 of 62 Page 180

In a ΔMNO, MP is the external bisector of ∠M meeting NO produced at P. If MN = 10 cm, MO = 6 cm, NO = 12 cm, then find OP.

Given: A MNO with MP as external bisector of M meeting NO produced at P, and MN = 10 cm, MO = 6 cm, NO = 12 cm

Required: Length of OP


In ΔMNP , MP is the external bisector of ∠M meeting NO ant produced at P.


Let OP = x cm , Now by angle bisector theorem, we have


⇒


⇒ (x + 12)×6 = 10x


⇒ 6x + 72 = 10x


⇒ 10x—6x = 72


⇒ 4x = 72


⇒ x = = 18


∴The value of x = 18 cm.


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