Question

If O is Any Point Inside a Rectangle Abcd Then `Oa^2+Oc^2=Ob^2+Od^2` 

Answer 1

 

Suppose ABCD is a rectangle with O is any point inside it.
Construction: `OA^2+OC^2=OB^2+OD^2` 

Proof: 

`OA^2+OC^2=OB^2+OD^2`                   [Using Pythagoras theorem in right triangle AOP and COQ] 

=`(BQ^2+OS^2)+(OQ^2+DS^2)` 

=`(BQ^2+OQ^2)+(OS^2+DS^2)`              [Using Pythagoras theorem in right triangle BOQ and DOS] 

=`OB^2+OD^2` 

Hence, LHS = RHS