Question

12
AB + BC + AC > 2AP.
In the given Figure, P is a point on the side BC of AABC. Prove that
AB+BC+AC >2AP​

Answer 1

Step-by-step explanation:

PROOF:-------:-------:--------

In trangle ABP,

AB + BP > AP -------eq. | [ Since, the sum of two sides of a triangle is always greater than the third side. ]

Similarly in triangle ACP,

AC +PC > AP -------eq.||

Now adding eq. | and || ,

We get; AB + BP + AC + PC > AP + AP

AB + ( BP + PC) + AC > 2AP

AB + BC + AC > 2AP; Hence Proved