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In a trapezium ABCD, if AB||CD then (AC^...

In a trapezium ABCD, if AB||CD then `(AC^(2)+BD^(2))=?`

A

`BC^(2)+AD^(2)+2BC*AD`

B

`AB^(2)+CD^(2)+2AB*CD`

C

`AB^(2)+CD^(2)+2AD*BC`

D

`BC^(2)+AD^(2)+2AB*CD`

Text Solution

Verified by Experts

The correct Answer is:
D

In `triangle ABC, angle B` is acute.
`therefore AC^(2)=BC^(2)+AB^(2)-2AB*AE.`
In `triangle ABD, angle A` is acute.
`therefore BD^(2)=AD^(2)+AB^(2)-2AB*BF`
`therefore (AC^(2)+BD^(2))=(BC^(2)+AD^(2))+2AB(AB-AE-BF)`
`=BC^(2)+AD^(2)+2AB*EF=BC^(2)+AD^(2)+2AB*CD.`
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