Question

o is a point in the rectangle AB C.D. Prove that oa²+oc²=ob²+od²​

Answer 1

Answer:

Here's your answer

Step-by-step explanation:

For figure see attachment

Let ABCD be the given rectangle with point O within it. Join OA, OB, OC, OD. Through O draw EOF||AB.Then ABFE is a rectangle.

In right ∆OEA and ∆OFC,

OA² = OE² + AE² and OC²= OF²+CF²

OA²+OC²=(OE²+AE²) +(OF²+CF²)

OA²+OC²=OE²+OF²+AE²+CF²………….(1)

In right ∆OFB and ∆ODE,

OB² = OF² + FB² and OD²= OE²+DE²

OB²+OD²=(OF²+FB²) +(OE²+DE²)

OB²+OD²=OE²+OF²+DE²+BF²

OB²+OD²=OE²+OF²+CF²+AE²…………..(2)

[DE=CF & AE=BF]

From eq i & eq ii,

OA² + OC² = OB² + OD²

Hope you understand.