O is any point inside a rectangle abcd prove That ob square+odsquare =oasquare+oc square
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Heya User,
Sorry ( I will avoid the use of a figure =_= )
--> Take the rectangle ABCD .
--> Take any interior point 'O'
--> Join OA, OB, OC, OD ...
Now, Draw EF || AB ( passing through O )
----> Also, GH || BC ( " " " )
----> E,F,G,H lies on the lines BC, AD, CD, AB respectively...
Note:-> Since, we had drawn ||s, the lengths :->
---> BE = OH ; GD = AH ; OE = GC || and good luck if uh wud find more of thm :sweat-smile:
----> :p || Apply Pythagoras and kill the problem :->
==> OB² + OD² = ( BE² + OE² ) + ( OG² + GD² )
= ( BE² + GD² ) + ( OG² + OE² )
= ( OH² + AH² ) + ( OG² + GC² )
= OA² + OC² :p <---- Your Proof...
Just to make uh aware, there are several other segments =_= or perhaps only few combinations that would help uh out but obviously, the idea used is the same...
Sorry ( I will avoid the use of a figure =_= )
--> Take the rectangle ABCD .
--> Take any interior point 'O'
--> Join OA, OB, OC, OD ...
Now, Draw EF || AB ( passing through O )
----> Also, GH || BC ( " " " )
----> E,F,G,H lies on the lines BC, AD, CD, AB respectively...
Note:-> Since, we had drawn ||s, the lengths :->
---> BE = OH ; GD = AH ; OE = GC || and good luck if uh wud find more of thm :sweat-smile:
----> :p || Apply Pythagoras and kill the problem :->
==> OB² + OD² = ( BE² + OE² ) + ( OG² + GD² )
= ( BE² + GD² ) + ( OG² + OE² )
= ( OH² + AH² ) + ( OG² + GC² )
= OA² + OC² :p <---- Your Proof...
Just to make uh aware, there are several other segments =_= or perhaps only few combinations that would help uh out but obviously, the idea used is the same...
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