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 exterior of a DeltaABC . Prove that 2(OA + OB + OC) > (AB + BC + CA) .

O is any point in the exterior of a DeltaABC . Prove that 2(OA + OB + OC) > (AB + BC + CA) .

O is any point in the interior of a triangle ABC. Prove that : OB + OC lt AB + AC. _Q01.png" width="60%">

If 'O' is any point in the interior of rectangle ABCD, then prove that : OB^(2) + OD^(2) = OA^(2) + OC^(2)

In the adjoining figure, P is an interior point of DeltaABC . Then prove that : AB+BC+CA lt 2(PA + PB +PC)

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 'O' is any point in the interior of rectangle ABCD,then prove that: OB^2+OD^2=OA^2+OC^2 .

O is any point in the interior of triangleABC such that OB=OC and AB=AC. Show that AO bisects angleA .

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