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In the given figure, ABCD is a quadrilateral such that DAAB and CBAB, x = y and EF || AD such that EF bisects DEC. Then CD2 is equal to


  1. Both (a) and (b)

  2. 2CE2

  3. 2DE2

  4. None of these


Solution

The correct option is A

Both (a) and (b)


Given,
ABCD is a quadrilateral with DAAB and CBAB
and EF || AD
EF||BC
EFAB
Now, in ΔDAE and ΔCBE,
DAE=CBE   [each 90]
Also, DEA=CEB
ΔDAEΔCBE   [by AA similarity]
DEAE=CEBEDE=CE    ...(i)
Now, in ΔDEC, right angled at E,
DE2+CE2=DC22DE2=2CE2=DC2

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