Question

In a quadrilateral ABCD, the diagonals AC, BD
intersect at right angles. Prove that:
AB² + CDP²= BC² +DA²​

Answer 1

Step-by-step explanation:

△AOB,

AB

2

=OA

2

+OB

2

......(1)

In △COD,

CD

2

=OC

2

+OD

2

.....(2)

In △OAD,

DA

2

=OA

2

+OD

2

......(3)

In △BOC,

BC

2

=OC

2

+OB

2

......(4)

Adding 1 & 2, we get,

AB

2

+CD

2

=OA

2

+OB

2

+OC

2

+OD

2

....(5)

Adding 3 & 4 , we get,

DA

2

+BC

2

=OA

2

+OB

2

+OC

2

+OD

2

......(6)

Form 5 & 6, we get,

AB

2

+CD

2

=BC

2

+DA

2

Answer 2

Answer: make as Brainly