O is any point inside the triangle ABC. Let’s prove thatAB+ACOB+OC

Question

O is any point inside the triangle ABC. Let’s prove thatAB+AC>OB+OC

Philoid · Accepted Answer

Let us first draw a diagram for the above proof.

We know one basic fact about triangles that the sum of any two sides of a triangle is always greater than the third side.

So let us first consider Δ ABC

AB + AC > BC ……………………. (i)

Similarly let us consider the Δ OBC

OB + OC >BC ……………………. (ii)

Now let us subtract equation (ii) from equation (i)

(AB + AC) – (OB + OC) > BC – BC

(AB + AC) – (OB + OC) > 0

AB + AC > OB + OC

Hence Proved.

O is any point inside the triangle ABC. Let’s prove that
AB+AC>OB+OC