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?

Question

AskiitiansExpert Abhinav Batra · Answer

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 · Answer

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^2

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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?

2 Answers

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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?

2 Answers

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Other Related Questions on Analytical Geometry

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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?