Published by:
CGP EDU Academic Team
Published on: August 13, 2026
Let ABCD be a rectangle and P be any point in its plane. Show that PA 2 + PC 2 = PB 2 + PD 2 .
Text Solution
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Sol.
L.H.S. PA 2 + PC 2 ( α – 0)
2 + ( β – 0) 2 + ( α – a) 2 + ( β – b) 2 = 2 α
2 + 2 β 2 – 2a α – 2b β + a 2 + b 2
R.H.S. PB 2 + PD 2
( α – a) 2 + ( β – 0) 2 + ( α – 0) 2 + ( β – b) 2 = 2 α
2 + 2 β 2 – 2a α – 2 b β + a 2 + b 2 PA
2 + PC 2 = PB 2 + PD 2
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