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by sanju09 » Tue Sep 14, 2010 6:09 am
B, C, E, and D are the points on a circle, in that order. If the chord BE intersects the chord CD in A, with AB = 4, BC = 6, AC = 5 and AD = 6; then what is the length of the chord DE?
(A) 6
(B) 7.5
(C) 8
(D) 9
(E) 10



translation of the [spoiler]Source: https://readyforgmat.com[/spoiler]
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by beatthegmatinsept » Tue Sep 14, 2010 8:19 am
sanju09 wrote:B, C, E, and D are the points on a circle, in that order. If the chord BE intersects the chord CD in A, with AB = 4, BC = 6, AC = 5 and AD = 6; then what is the length of the chord DE?
(A) 6
(B) 7.5
(C) 8
(D) 9
(E) 10



translation of the [spoiler]Source: https://readyforgmat.com[/spoiler]
Since BE and CD are intersecting lines, vertical angles BAC = DAE.
This means the sides of the triangle opposite equal angles are also equal. (Consider triangles BAC and DAE).
This would mean that BC = DE = 6. (A)
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by euro » Tue Sep 14, 2010 8:41 am
sanju09 wrote:B, C, E, and D are the points on a circle, in that order. If the chord BE intersects the chord CD in A, with AB = 4, BC = 6, AC = 5 and AD = 6; then what is the length of the chord DE?
(A) 6
(B) 7.5
(C) 8
(D) 9
(E) 10



translation of the [spoiler]Source: https://readyforgmat.com[/spoiler]



I am getting DE=9 as the answer. Heres how I solved...
Triangles BAC and DAE are similar traingles. Therefore, their sides should be in proportion to each other.
(AD/AB) = (DE/BC)
=> (6/4) = (DE/6)
=> DE = 36/4 = 9

Please confirm whether this is right or wrong?
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Last edited by euro on Tue Sep 14, 2010 11:41 am, edited 1 time in total.
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by diebeatsthegmat » Tue Sep 14, 2010 11:10 am
beatthegmatinsept wrote:
sanju09 wrote:B, C, E, and D are the points on a circle, in that order. If the chord BE intersects the chord CD in A, with AB = 4, BC = 6, AC = 5 and AD = 6; then what is the length of the chord DE?
(A) 6
(B) 7.5
(C) 8
(D) 9
(E) 10



translation of the [spoiler]Source: https://readyforgmat.com[/spoiler]
Since BE and CD are intersecting lines, vertical angles BAC = DAE.
This means the sides of the triangle opposite equal angles are also equal. (Consider triangles BAC and DAE).
This would mean that BC = DE = 6. (A)
hey guy, can you draw the circle with it polygon?
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by ankur.agrawal » Tue Sep 14, 2010 11:41 am
euro wrote:
sanju09 wrote:B, C, E, and D are the points on a circle, in that order. If the chord BE intersects the chord CD in A, with AB = 4, BC = 6, AC = 5 and AD = 6; then what is the length of the chord DE?
(A) 6
(B) 7.5
(C) 8
(D) 9
(E) 10



translation of the [spoiler]Source: https://readyforgmat.com[/spoiler]
I am getting DE=9 as the answer. Heres how I solved...
Triangles BAC and DAE are similar traingles. Therefore, there sides should be in proportion to each other.
(AD/AB) = (DE/BC)
=> (6/4) = (DE/6)
=> DE = 36/4 = 9

Please confirm whether this is right or wrong?
I agree with euro. I agree on 9 by making the two triangles similar.

Euro can u confirm how do you make Angle ABC = Angle ADE. I did it by using the Incribed angle properties.Can u comment
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by euro » Tue Sep 14, 2010 11:46 am
ankur.agrawal wrote:
euro wrote:
sanju09 wrote:B, C, E, and D are the points on a circle, in that order. If the chord BE intersects the chord CD in A, with AB = 4, BC = 6, AC = 5 and AD = 6; then what is the length of the chord DE?
(A) 6
(B) 7.5
(C) 8
(D) 9
(E) 10



translation of the [spoiler]Source: https://readyforgmat.com[/spoiler]
I am getting DE=9 as the answer. Heres how I solved...
Triangles BAC and DAE are similar traingles. Therefore, there sides should be in proportion to each other.
(AD/AB) = (DE/BC)
=> (6/4) = (DE/6)
=> DE = 36/4 = 9

Please confirm whether this is right or wrong?
I agree with euro. I agree on 9 by making the two triangles similar.

Euro can u confirm how do you make Angle ABC = Angle ADE. I did it by using the Incribed angle properties.Can u comment
i edited my previous post to include a figure (A Circle with two chords BE and CD cutting each other at point A). But moderator has blocked the post for screening the content.

Once mod clears and allows the image to be uploaded, things should become clearer.
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by ankur.agrawal » Tue Sep 14, 2010 11:58 am
I have attached a diagram. See if it clear enough to clear d question.
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Circle.jpg
Hazy diagram attached
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by ankur.agrawal » Tue Sep 14, 2010 12:07 pm
Can a expert comment please.
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by goyalsau » Tue Sep 14, 2010 12:31 pm
ankur.agrawal wrote:
euro wrote:
sanju09 wrote:B, C, E, and D are the points on a circle, in that order. If the chord BE intersects the chord CD in A, with AB = 4, BC = 6, AC = 5 and AD = 6; then what is the length of the chord DE?
(A) 6
(B) 7.5
(C) 8
(D) 9
(E) 10



translation of the [spoiler]Source: https://readyforgmat.com[/spoiler]
I am getting DE=9 as the answer. Heres how I solved...
Triangles BAC and DAE are similar traingles. Therefore, there sides should be in proportion to each other.
(AD/AB) = (DE/BC)
=> (6/4) = (DE/6)
=> DE = 36/4 = 9

Please confirm whether this is right or wrong?
I agree with euro. I agree on 9 by making the two triangles similar.

Euro can u confirm how do you make Angle ABC = Angle ADE. I did it by using the Incribed angle properties.Can u comment
Nice to see that you guys actually put in images,
but just wondering is this is a property of a circle that with any two intersecting cord the triangles that will be formed with be similar, because i am not able to any other way to solve this problem......
If there is a property that this question is done in a bit and will brought forward to the 51 mark, but if its not then please the reasoning.........behind it,
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by sanju09 » Tue Sep 14, 2010 11:54 pm
A handy piece of information on the subject of circle...

If two chords BE and CD of a circle intersect inside or outside the circle (when produced) at a point A, then

BA × AE = CA × AD



[spoiler]OA is D[/spoiler]
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