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A chord of a circle is 15 centimeters from the circle’s center. If the

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Bunuel
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A chord of a circle is 15 centimeters from the circle’s center. If the [#permalink] New post   26 Apr 2018, 13:31
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A chord of a circle is 15 centimeters from the circle’s center. If the circle’s radius is 17 centimeters, what is the chord’s length, in centimeters?

(A) 7.5
(B) 8
(C) 9.5
(D) 12
(E) 16
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pushpitkc
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Re: A chord of a circle is 15 centimeters from the circle’s center. If the [#permalink] New post   26 Apr 2018, 13:40
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Bunuel wrote:
A chord of a circle is 15 centimeters from the circle’s center. If the circle’s radius is 17 centimeters, what is the chord’s length, in centimeters?

(A) 7.5
(B) 8
(C) 9.5
(D) 12
(E) 16


Attachment:
Circle_Chord-CD.png
Circle_Chord-CD.png [ 3.1 KiB | Viewed 1704 times ]


In the figure given above, we are given the following information

Length of chord from the circle's center(OX) = 15
Radius of the circle(OD) = 17

In right angled triangle OXD, \(OD^2 = OX^2 + XD^2\)
\(XD^2 = 17^2 - 15^2 = 289 - 225 = 64\) -> \(XD = \sqrt{64} = 8\)

Therefore, the length of the chord CD is twice the length of XD or 16(Option E)
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Re: A chord of a circle is 15 centimeters from the circle’s center. If the [#permalink] New post   15 May 2018, 06:35
pushpitkc wrote:
Bunuel wrote:
A chord of a circle is 15 centimeters from the circle’s center. If the circle’s radius is 17 centimeters, what is the chord’s length, in centimeters?

(A) 7.5
(B) 8
(C) 9.5
(D) 12
(E) 16


Attachment:
Circle_Chord-CD.png


In the figure given above, we are given the following information

Length of chord from the circle's center(OX) = 15
Radius of the circle(OD) = 17

In right angled triangle OXD, \(OD^2 = OX^2 + XD^2\)
\(XD^2 = 17^2 - 15^2 = 289 - 225 = 64\) -> \(XD = \sqrt{64} = 8\)

Therefore, the length of the chord CD is twice the length of XD or 16(Option E)



the length of the chord CD is twice the length of XD or [color=#00a651]16(Option E)

For above statement, it has used property of circle-
Perpendicular from centre of circle to chord bisect the chord into two equal parts.

That's why length of chord is twice length of XD

Give kudos if it helps

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A chord of a circle is 15 centimeters from the circle’s center. If the [#permalink] New post   15 May 2018, 09:02
Use simple Pythegorean formula (Best if you know Pythegorean Triples : https://www.friesian.com/pythag.htm )

The answer can be solved immediately after diagramming the Question, must be (E) 16
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A chord of a circle is 15 centimeters from the circle’s center. If the [#permalink]
15 May 2018, 09:02
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