Question

For the following statement, state whether true (T) or false (F): 

If O is any point inside a rectangle ABCD then OA² + OC² = OB² + OD². 

Answer 1

This statement is true.

Explanation:

 

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