Side of a triangle

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lilu: Master | Next Rank: 500 Posts; Posts: 148; Joined: Wed Dec 10, 2008 5:13 pm; Location: SF, CA; Thanked: 12 times

by lilu » Tue Mar 03, 2009 11:21 pm

In the figure to the right, if point C is the center of the circle and DB = 7, what is the length of DE?

(1) x = 60°

(2) DE || CA

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Source: Beat The GMAT — Data Sufficiency | Tue Mar 03, 2009 11:21 pm

quocbao: Senior | Next Rank: 100 Posts; Posts: 88; Joined: Tue Mar 03, 2009 8:10 am; Thanked: 3 times

by quocbao » Wed Mar 04, 2009 12:14 am

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

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scoobydooby: Legendary Member; Posts: 1035; Joined: Wed Aug 27, 2008 10:56 pmFollowed by: 1 member; Thanked: 104 times

by scoobydooby » Wed Mar 04, 2009 5:16 am

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: MBA Student; Posts: 1194; Joined: Sat Aug 16, 2008 9:42 pmFollowed by: 17 members; Location: Paris, France; Thanked: 71 times; GMAT Score:710

Answer is D

by gmat740 » Wed Mar 04, 2009 7:18 am

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

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quocbao: Senior | Next Rank: 100 Posts; Posts: 88; Joined: Tue Mar 03, 2009 8:10 am; Thanked: 3 times

by quocbao » Wed Mar 04, 2009 8:22 am

Thanks gmat740. I just don't remember many things

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