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Consider a rectangle ABCD . Let P be any point in the plane of this rectangle. Prove that PA 2 + PC 2 = PB 2 + PD 2 (plzz can u xplain with diagram)Can u also tell me what TONCAS means and what is its significance in this problem?

 



Consider a rectangle


ABCD.


 Let P be any point in the plane of this rectangle.


Prove that



PA2 + PC2 = PB2 + PD2(plzz can u xplain with diagram)Can u also tell me what TONCAS means and what is its significance in this problem?

Grade:10

2 Answers

AskiitiansExpert Abhinav Batra
25 Points
14 years ago

construct a line parralel to AD through P

use pythagoras theorem

pa^2=pe^2+ae^2

pb^2=be^2+pe^2

pc^2=pf^2+cf^2

pd^2=pf^2+fd^2

 

but AE=FD

EB=FC

 

so PA^2+PC^2=PB^2+PD^2

AskiitiansExpert Abhinav Batra
25 Points
14 years ago

construct a line parallel to AD through P and let it intersect AB at E and CD at F

use pythagoras theorem

pa^2=pe^2+ae^2

pb^2=pe^2+be^2

pc^2=pf^2+cf^2

pd^2=pf^2+df^2

 

 

AE=FD && BE=CF

So PA^2+PC^2=PE^2+PF^2+AE^2+CF^2=PE^2+PF^2+FD^2+BE^2=PB^2+Pd^21793_14504_rectangle.jpg

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