Correct Option: B

As per given figure , we can see that
Since the diagonals of a rectangle are equal and bisect each other. Let AC and BD intersect at M. Therefore M is the mid-point of AC and BD and AM = DM
From ΔAOC, OA² + OC² = 2(AM² + MO²) [Appollonius Theorem.] .......... ( 1 )
also in ΔODB, OB² + OD² = 2(MO² + DM²) = 2(MO² + AM²) .......... ( 2 )
From equations ( 1 ) and ( 2 ) .
∴ OA² + OC² = OB² + OD².