Question

A point O in the interior of a rectangle ABCD is joined to each of the vertices A, B, C,D. prove that OBsq + ODsq = OCsq + OAsq

Answer 1

From point O, draw perpendiculars  OE, OF, OG, OH onto the sides AB, BC, CD and DA respectively.

Use Pythagoras theorem.  
OA² = OE² + OH² 
OB² = OE² + OF²
OC² = OF² + OG²
OD² = OG² + OH²

So if you add the LHS , you find the RHS.

Answer 2

From point O, draw perpendiculars  OE, OF, OG, OH onto the sides AB, BC, CD and DA respectively.

Use Pythagoras theorem.  

OA² = OE² + OH² 

OB² = OE² + OF²

OC² = OF² + OG²

OD² = OG² + OH²

So if you add the LHS , you find the RHS.