Q4 A of 59 Page 194

P is any point inside ABC let’s prove that,
AP+BP>AB

Let us first draw a figure for the above question.

P is any point inside the Δ ABC.

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

Now let us consider the Δ APB

AP + BP > AB

Hence Proved.

O is any point inside the triangle ABC. Let’s prove that

AB+BC+AC>OA+OB+OC

Let’s prove that the perimeter of a quadrilateral is more than twice of the sum length of any diagonal.

4 B

P is any point inside ABC let’s prove that,

AB+BC+AC<2(AP+BP+CP)

Let’s prove that the perimeter of a triangle is more than the sum of length of the medians.

P is any point inside ABC let’s prove that,AP+BP>AB