Q. 2 B5.0( 2 Votes )

# O is any point in

From the above proof, we have

AB + AC > OB + OC …….. (I)

Let us modify the above figure a bit by connecting OA Now from Δ ABC

AC + BC > AB ……….. (i)

Similarly from Δ OAB

OA + OB > AB ………. (ii)

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

AC + BC – (OA + OB) > AB – AB

AC + BC – (OA + OB) > 0

AC + BC > OA + OB ………….. (II)

Now let us again consider Δ ABC,

AB + BC > AC ………….. (iii)

Similarly from Δ OAC

OA + OC > AC …………. (iv)

Now let us subtract equation (iv) from equation (iii)

AB + BC – (OA + OC) > AC – AC

AB + BC – (OA + OC) > 0

AB + BC > OA + OC ……. (III)

Now let us add equations (I), (II) and (III)

AB + BC + AC + BC + AB + AC > OB + OA + OA + OC + OC + OB

2AB + 2BC + 2AC > 2OB + 2OC + 2OA

2 (AB + BC + AC) > 2 (OB + OC + OA)

(AB + BC + AC) > (OB + OC + OA)

Hence Proved.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses RELATED QUESTIONS :

Let’s write then West Bengal - Mathematics

Let’s write then West Bengal - Mathematics

Let’s write then West Bengal - Mathematics

Let’s write whethWest Bengal - Mathematics

let’s find whetheWest Bengal - Mathematics

Let’s find whetheWest Bengal - Mathematics

Let's observe theWest Bengal - Mathematics

let’s write whethWest Bengal - Mathematics

Let’s write the sWest Bengal - Mathematics

Let's prove logicWest Bengal - Mathematics