Any Point Equidistant from the End Points of a Segment Lies on the Perpendicular Bisector of the Segment
If O is any p...
Question
If O is any point within △ABC,then to prove that AB + BC + CA > AO + BO + CO
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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