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# What's the chord of a circle?

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Senior Manager
Joined: 17 May 2005
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What's the chord of a circle? [#permalink]

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10 Jun 2005, 18:09
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

I got this question wrong cuz i didn't know what the chord of a circle was...

Given that AB and CD are two chords of a circle intersecting at the point O outside the circle, and AB = 7 m, BO = 5 m, and OD = 3 m. Find the lengt hof OC.

A. 20 m
B. 16 m
C. 35 m
D. 6 m
E. 18 m
Director
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Re: What's the chord of a circle? [#permalink]

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10 Jun 2005, 18:55
cloudz9 wrote:
I got this question wrong cuz i didn't know what the chord of a circle was...

Given that AB and CD are two chords of a circle intersecting at the point O outside the circle, and AB = 7 m, BO = 5 m, and OD = 3 m. Find the lengt hof OC.

A. 20 m
B. 16 m
C. 35 m
D. 6 m
E. 18 m

B. maybe

Diameter is greater than 7 and less than 14, so CD+3 is less than 17 => 16
CD got to be relatively close to the center of the circle for this to happen, excluding D

how do you solve it directly?

Last edited by sparky on 10 Jun 2005, 19:01, edited 1 time in total.
Senior Manager
Joined: 17 May 2005
Posts: 272
Location: Auckland, New Zealand
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Re: What's the chord of a circle? [#permalink]

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10 Jun 2005, 19:00
sparky wrote:
cloudz9 wrote:
I got this question wrong cuz i didn't know what the chord of a circle was...

Given that AB and CD are two chords of a circle intersecting at the point O outside the circle, and AB = 7 m, BO = 5 m, and OD = 3 m. Find the lengt hof OC.

A. 20 m
B. 16 m
C. 35 m
D. 6 m
E. 18 m

Frankly i have no idea...i mean i though i knew what a chord was...a line which passes through a circle...
but i couldn't solve the question...

here's how the OA goes
maybe you can make more sense of it than i could

If BO = 5, then AO = 5 + 7 = 12 cm.
We also know that,
AO * BO = CO * DO
or, 12 * 5 = CO * 3
or, CO = 60 / 3 = 20

I'm not sure why AO*BO is equal to CO*DO

maybe someone who's better versed in geometry can help me out...

is it some theorem i didn't know about...or am i missing something here
Director
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10 Jun 2005, 19:04
there is theorem that says

AO * BO = OC * OD

12 * 5 = OC * 3

OC = 20
Director
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10 Jun 2005, 19:14
I think this can be shown if you extend lines from te center of the circle to A, B, C, and D,
connect A and C and B and D, compare angles and show that some triangles are similar.
Director
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10 Jun 2005, 19:57
As an extension to this, if you have a tangent to a circle intersecting with a chord to the circle at an external point,

then (oA)^2 = OC*OD ( where A is the point of contact of the tangent with the circle, C and D are points where chord intersects the circle)
Senior Manager
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10 Jun 2005, 20:33
Vithal wrote:
As an extension to this, if you have a tangent to a circle intersecting with a chord to the circle at an external point,

then (oA)^2 = OC*OD ( where A is the point of contact of the tangent with the circle, C and D are points where chord intersects the circle)

Interesting...

learn something new everyday on this forum!

SVP
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10 Jun 2005, 20:40
Ahh this is a good one. Here we can use the concept of cyclic quadrilateral that we just learned yesterday.

A cyclic quadrilateral is a quadrilateral for which a circle can be circumscribed so that it touches each polygon vertex.
The opposite angles of a cyclic quadrilateral sum to 180 degrees.

In other words, angel ABD + angel ACD=180
Also since angel ABD+angel ABO=180
Therefore angel ABO=angel ACD
Now we have triangle AOC is similar to triangle DOB
Therefore AO/CO=DO/BO

From here you'll get the OA explanation that says AO * BO = OC * OD and thus solve for OC.
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10 Jun 2005, 20:40
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