In a quadrilateral ABCD, it is given that AB || CD and the diagonals AC and BD are perpendicular to each other. Show that
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
. 
= 0
Also µ 
– 
| | 
– 
⇒ µ = λ .
| 
– 
| | µ 
– 
| ≥ |( 
– 
)| |( 
–µ 
)|
⇒ ( λ 2 b 2 + a 2 )(µ 2 a 2 + b 2 ) ≥ (b 2 + a 2 )( λ 2 b 2 + µ 2 a 2 )
⇒ λ 2 µ 2 a 2 b 2 + a 2 b 2 ≥ λ 2 a 2 b 2 + µ 2 b 2 a 2
⇒ ( λ 2 – 1) (µ 2 – 1) ≥ 0
⇒ ( λ 2 – 1) 2 ≥ 0 which is true.
(AD + BC) 2 ≥ (AB + CD) 2
⇒ AD 2 + OD 2 + OC 2 + OB 2 + 2AD.BC ≥ OA 2 + OB 2 + OD 2 + OC 2 + 2AB. CD
which follows from .
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