ABCD is a rectangle Draw EF || AB ||CD passing through O
Here,DE = CF and AE = BF...(1) In right ΔOBF, OB2=BF2+OF2....(2) In right ΔODE, OD2=DE2+OE2...(3) In right ΔOCF, OC2=CF2+OF2....(4) In right ΔOAE, OA2=AE2+OE2....(5) Adding (2) and (3), we get
OB2+OD2=BF2+OF2+DE2+OE2
=AE2+OF2+CF2+OE2 =OA2+OC2 [Using (1), (4) and (5)]