Question

‘O’ is any point inside a rectangle ABCD. Prove that OB² + OD² = OA² + OC²

Answer 1

Answer:

OB² + OD² = OA² + OC²

Step-by-step explanation:

Lets draw ⊥ on AB  & CD  such that it divides AB into a  & b two parts

& its height are x  & y

OB² = x² + b²

OD² = y² + a²

OB² + OD² = x² + b² + y² + a²

=> OB² + OD² = x² + y² + a² + b²

OA² = x² + a²

OC² = y² + b²

OA² + OC²  =  x² + a² + y² + b²

=> OA² + OC²  =  x² + y² + a² + b²

=> OB² + OD² = OA² + OC²