Question

Is this statement true: If P is a point on the side of BC of triangle ABC. Then (AB+BC+AC)>2AP.

Answer 1

Answer:

Yes

Step-by-step explanation:

Join AP

You will observe two triangles ΔAPB and Δ ACP

In Δ APB

AB + BP > AP  -- (i)  [In a Δ sum of two sides is always greater than third side]

In Δ ACP

AC + PC > AP --- ( ii ) [In a Δ sum of two sides is always greater than third side]

Adding Eq( i ) and ( ii )

AB + BP + AC + PC > AP + AP

(AB + BC + AC) > 2 AP      [ ∵ BP + PC = BC]