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

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Bunuel
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Given that AB and CD are two chords of a circle intersecting at the po [#permalink] Given that AB and CD are two chords of a circle intersecting at the po   08 Feb 2021, 06:00
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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. What is the length of OC ?


A. 6 m
B. 16 m
C. 18 m
D. 20 m
E. 35 m
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D
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meanup
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Re: Given that AB and CD are two chords of a circle intersecting at the po [#permalink] Given that AB and CD are two chords of a circle intersecting at the po   08 Feb 2021, 06:29
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Intersecting secants theorem, \(AO*OB=OD*OC\)

\((7+5)*5=3*OC\)
\(4*5=OC\)

\(OC=20\)

Ans D
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CEdward
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Re: Given that AB and CD are two chords of a circle intersecting at the po [#permalink] Given that AB and CD are two chords of a circle intersecting at the po   11 Feb 2021, 21:19
meanup wrote:
Intersecting secants theorem, \(AO*OB=OD*OC\)

\((7+5)*5=3*OC\)
\(4*5=OC\)

\(OC=20\)

Ans D


meanup Can you elaborate on this a little more? I get the math, but just want to understand the theory a little more.
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Given that AB and CD are two chords of a circle intersecting at the po [#permalink] Given that AB and CD are two chords of a circle intersecting at the po   11 Feb 2021, 21:51
CEdward wrote:
Can you elaborate on this a little more? I get the math, but just want to understand the theory a little more.


CEdward

If I'm not mistaken the theorem is called "Secants Theroem"

Here, are some better explanation from Google. Or, you could google it, else, refer to Bunuel post: https://gmatclub.com/forum/math-circles-87957.html which will come handy when dealing with circle.
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Re: Given that AB and CD are two chords of a circle intersecting at the po [#permalink] Given that AB and CD are two chords of a circle intersecting at the po   25 Aug 2023, 03:30
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