Let O be any point in the interior of `DeltaABC`, prove that :
`AB+BC+CA lt 2 (OA+OB+OC)`

'O' is any point in the interior of a Delta ABC prove that AB+BC+CA>OA+OB+OC

O is any point in the interior of ABC .Prove that AB+AC>OB+OCAB+BC+CA>OA+OB+OCOA+OB+OC>(1)/(2)(AB+BC+CA)

If G be the centroid of the DeltaABC and O be any other point in theplane of the triangle ABC , then prove that: OA^2 +OB^2 +OC^2=GA^2 +GB^2 +GB^2 + GC^2 + 3GO^2

If O is point in the exterior of triangleABC ,show that 2(OA+OB+OC)gt(AB+BC+CA)

Let O be an interior point of Delta ABC such that 2vec OA+5vec OB+10vec OC=vec 0

If O is the circumcentre and P the orthocentre ( of Delta ABC, prove that )/(OA)+vec OB+vec OC=vec OP

In DeltaABC, D is any point on side BC. Prove that AB+BC+CA gt 2AD

In DeltaABC, if D is any point on the side BC, show that (AB+BC+AC)gt 2AD.

Let O be an interior point of DeltaABC such that bar(OA)+2bar(OB) + 3bar(OC) = 0. Then the ratio of a DeltaABC to area of DeltaAOC is