(C)

From the above figure we get that,

AE = AD + DE

CB = CD + DB

And it is given is that AE = CB

So,

AD + DE = CD + DB

AD + CD= CD + DB………….(i) [DE = CD as given]

According to Euclid’s axiom, when equals are subtracted from equals, the remainders are also equal.

Subtracting CD from both side in eq (i), we get

AD + CD − CD = CD + DB − CD

AD = DB

So, D is the mid-point of line segment AB.