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
Side of a triangle
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Source: Beat The GMAT — Data Sufficiency |
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scoobydooby
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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
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
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gmat740
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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
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
