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AB and CD are two chords of a circle intersecting at the

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AB and CD are two chords of a circle intersecting at the [#permalink]

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02 Dec 2005, 11:50
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

AB and CD are two chords of a circle intersecting at the point E outside the circle so that
B and D are closer to E. If BE = 3 inches, AB = 5 inches, and ED = 4 inches, what is the
length of CD in inches?
(A) 2
(B) 5
(C) 6
(D) 7
(E) 8
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02 Dec 2005, 16:13
AE/CE=ED/EB let CE be x and AE=AB+BE=8

8/x=4/3 24=4x; x=CE=6

CE=ED+DC; DC=CE-ED=6-4=2
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02 Dec 2005, 20:09
rlevochkin wrote:
AE/CE=ED/EB let CE be x and AE=AB+BE=8

8/x=4/3 24=4x; x=CE=6

CE=ED+DC; DC=CE-ED=6-4=2

great, you remember that similar-triangle rule of a circle!! ..i'm going to draw and prove how it works
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02 Dec 2005, 20:25
if you're interested in
btw, hadzamir, i find your geo problems very interesting. Can you let me know the source or post more here?!! Thanks
Attachments

similar.doc [25.5 KiB]

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03 Dec 2005, 03:32
rlevochkin wrote:
AE/CE=ED/EB let CE be x and AE=AB+BE=8

8/x=4/3 24=4x; x=CE=6

CE=ED+DC; DC=CE-ED=6-4=2

thanks
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03 Dec 2005, 04:23
laxieqv wrote:
if you're interested in
btw, hadzamir, i find your geo problems very interesting. Can you let me know the source or post more here?!! Thanks

one thing in your prove that i don't get:
why do you assume that ab and cd intersect in point O which is the center of the circle, or in other word - why do you assume that angle DOA is 180 degrees (why AD is a straight line?) same with line CB of course.
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03 Dec 2005, 04:32
laxieqv wrote:
if you're interested in
btw, hadzamir, i find your geo problems very interesting. Can you let me know the source or post more here?!! Thanks

one thing in your prove that i don't get:
why do you assume that ab and cd intersect in point O which is the center of the circle, or in other word - why do you assume that angle DOA is 180 degrees (why AD is a straight line?) same with line CB of course.

Did i say so?! ..You should look more carefully at my illustration
The first part i was trying to prove that every angle form by two ends of a cord and a certain point in the circle is always = 1/2 angle formed by that cord's ends and the circle's centre ( This is a basic principle of geometry)
Then, i apply this rule to get DAB = DCB , COZ they're both =1/2 DOC ( YOU have to imagine this centre on your own, i don't put it in my illustration)

Again, there's nothing related to O in the second figure.
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03 Dec 2005, 04:58
laxieqv wrote:
laxieqv wrote:
if you're interested in
btw, hadzamir, i find your geo problems very interesting. Can you let me know the source or post more here?!! Thanks

one thing in your prove that i don't get:
why do you assume that ab and cd intersect in point O which is the center of the circle, or in other word - why do you assume that angle DOA is 180 degrees (why AD is a straight line?) same with line CB of course.

Did i say so?! ..You should look more carefully at my illustration
The first part i was trying to prove that every angle form by two ends of a cord and a certain point in the circle is always = 1/2 angle formed by that cord's ends and the circle's centre ( This is a basic principle of geometry)
Then, i apply this rule to get DAB = DCB , COZ they're both =1/2 DOC ( YOU have to imagine this centre on your own, i don't put it in my illustration)

Again, there's nothing related to O in the second figure.

you are right, now i get it. THANKS!!!
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03 Dec 2005, 05:07
your geo problems are very interesting!! Can you please tell me the source or post more of them?! Thank you.
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03 Dec 2005, 06:51
laxieqv wrote:
your geo problems are very interesting!! Can you please tell me the source or post more of them?! Thank you.

they are not from a book. i got them from a friend of mine (the paper called "hard questions"), but the real hard questions i have published here and i will continue to publish if i'll encounter with more.
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03 Dec 2005, 07:14
thank you ..and i'm sorry if my attitude was not friendly just now..i'm now much stressful due to my upcoming finals
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03 Dec 2005, 09:37
i got CD=20/3 ? BD is parallel to AC, hence EB/EA=ED/EC ! so 3/8=4/(4+x) => x=20/3 ! what i am missing ?
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03 Dec 2005, 09:56
christoph wrote:
i got CD=20/3 ? BD is parallel to AC, hence EB/EA=ED/EC ! so 3/8=4/(4+x) => x=20/3 ! what i am missing ?

you're missing from the bold part, buddy ...the two lines can't always be parallel
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