wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If O is any point within ABC,then to prove that AB + BC + CA > AO + BO + CO

Open in App
Solution

Let us ABC and mark point O anywhere inside the triangle.

Now, there is a known inequality:
AO + CO < AB + BC (Proof can be given, if you need)
Similarly,
AO + BO < AC + BC
BO + CO > AB + AC
Adding all these together, we get,
2(AO + BO + CO) < 2 (AB + BC + CA)
AB+BC+CA>AO+BO+CO

flag
Suggest Corrections
thumbs-up
2
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Any Point Equidistant from the End Points of a Segment Lies on the Perpendicular Bisector
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon