UPSC CDS Math Quadrilateral and Polygon Questions

ABCD is a rectangle
Draw EF || AB ||CD passing through OHere,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
=AE2+OF2+CF2+OE2
=OA2+OC2
[Using (1), (4) and (5)]