Question

prove that-AP =1/3AC​

Answer 1

Answer:

Please tell full question

Answer 2

prove that-AP =1/3AC​

The complete question is:

M is mid point of side BC of triangle ABC .N is the mid point of AM . BN when produced meets AC at P . prove that AP =1\3AC

Consider the attached figure while going through the following steps:

Given,

M is mid point of side BC

N is mid point of side AM.

Contruction: Draw a line MO ║ BP

In  Δ BPC

M is mid-point of BC

MO ║ BP

O is the mid-point of CP

⇒ OC = OP  ----- (1)

In Δ AMO

N is the mid-point of AM

NP ║ MO

P is the mid-point of AO

⇒  AP = PO ----- (2)

From equations (1) and (2),

We get, AP = PO = OC

⇒ AC = AP + PO + OC

⇒ AC = AP + AP + AP

⇒ AC = 3AP

∴ AP= 1/3AC