Mathematics
If O is any point in the interior of a triangle ABC, show that OA + OB + OC > (AB + BC + CA).
Triangles
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Answer
In △OBC, OB + OC > BC ……(i) (As sum of any two sides of triangle > third side)
Similarly OC + OA > CA …….(ii)
and, OA + OB > AB …….(iii)
On adding (i), (ii) and (iii), we get
⇒ OB + OC + OC + OA + OA + OB > BC + CA + AB
⇒ 2(OA + OB + OC) > AB + BC + CA
⇒ OA + OB + OC > (AB + BC + CA).
Hence, proved that OA + OB + OC > (AB + BC + CA).
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