Question

O is an interior point of triangle ABC. bo meets AC at D. show that OB+OC<AB+AC

Answer 1

Construction: Produce BO to meet AC in D.



Proof: The sum of any two sides of a triangle is greater than the third side.
In ΔABD, AB + AD > BD

⇒ AB + AD > BO + OD ----------------- (1)

In ΔOCD, CD + DO > OC -------------- (2)
[Sum of any two sides must be greater than the third side.]

Adding equations (1) and (2), we get
AB + AD + CD + DO > BO + OD + OC
⇒ AB + AC + DO > BO + OD + OC
⇒ AB + AC > OB + OC

Hence proved