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