O is any interior point in triangle ABC .prove that OA+OB+OC > 1/2(AB+BC+CA)
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you might be aware of triangle inequality
oa + ob > ab
ob + oc > bc
oa + oc > ac
add them
2(oa + ob + oc ) > ab + bc + ca
hence
oa + ob + oc > 1/2(ab + bc + ca)
oa + ob > ab
ob + oc > bc
oa + oc > ac
add them
2(oa + ob + oc ) > ab + bc + ca
hence
oa + ob + oc > 1/2(ab + bc + ca)
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