Answer :

Construction: Join CF and extent it to cut AB at point M

Firstly, in triangle MFB and triangle DFC


DF = FB (As F is the mid-point of DB)


DFC = MFB (Vertically opposite angle)


DFC = FBM (Alternate interior angle)


By ASA congruence rule


∆MFB DFC


Now, in triangle CAM


E and F are the mid-points of AC and CM respectively


EF = 1/2 (AM)


EF = 1/2 (AB – MB)


EF = 1/2 (AB-CD)


Hence, option D is correct

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