Given: In ABCD, O is any point within the quadrilateral.
To prove:
Proof:

We know that the sum of any two sides of a triangle is greater than the third side.
So, in ∆AOC,

OA + OC > AC …(1)

Also, in ∆ BOD,

OB + OD > BD …(2)

Adding 1 and 2, we get,

(OA + OC) + (OB + OD) > (AC + BD)
∴ OA + OB + OC + OD > AC + BD

Hence proved.