Side of a triangle

It is C.

At first I think that I is sufficient but when i look at II, I change my mind. II tells us that EDB = X = 60* , then DEB is equilateral triangle => DE = DB

B

1) x = 60°,
-since DB is the diameter, DC=CB, also CB=CA (radius)

-in triangle ACB, x=60° and angles CAB and CBA are equal (angles opposite equal sides)
=>triangle ACB is equilateral,all angles are 60° (sum of all angles of a triangle is 180)
=>AC=CB=AB=3.5
but we do not know if AC is || to DE or if A is the midpoint of EB, cant say what is the lenghth of DE. not sufficient


2) DE || CA
applying midpoint theorem: line joining the midpoints of opposite sides of a triangle is parallel to the third side and is 1/2 of the third side

C is the midpoint of DB, AC|| to DE
applying the converse of the theorem, A must be the midpoint of BE and AC must be half of DE
AC=3.5
DE=2*3.5=7
sufficient

hence B

Take a look

1) x= 60

So the triangle ABC is an equilateral triangle
( AC=BC ;radius
and Since angle A and B are equal, {angles opposite to equal sides}

and x=60....so rest both the angles are also 60)

Since chords from external point are equal,so ED=EB
thus < B=<D

But <B is already 60(equilateral triangle)

SO <D also comes out to be 60

and hence the only angle left E also becomes 60.
So this triangle EDB is also equilateral triangle,hence ED=DB=7

2) ) DE || CA
applying midpoint theorem: line joining the midpoints of opposite sides of a triangle is parallel to the third side and is 1/2 of the third side

C is the midpoint of DB, AC|| to DE
applying the converse of the theorem, A must be the midpoint of BE and AC must be half of DE
AC=3.5
DE=2*3.5=7
sufficient

SO both alone are sufficent
Answer is D

Thanks gmat740. I just don't remember many things