My Math Forum Looking for a formula to calculate a chord length

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July 23rd, 2013, 07:25 AM   #1
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Looking for a formula to calculate a chord length

I am sorry to post such a lame question to all you fine people, but you either know or you don't...and I don't.
What I am looking for is a formula that calculates the length X shown in the picture attached. I am given 'Y' dimension and Diameter 'D' only
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July 23rd, 2013, 09:44 AM   #2
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Re: Looking for a formula to calculate a chord length

Hello, rainycat!

Quote:
 $\text{Given: length }y,\:\text{ diameter }d. \;\;\;\text{Find length }x.$ Code:  A * o * * |y * B o - - - o - - - o C * * D| x * * * | * r * * | * * * o * * O * * * * *

$\text{W\!e have: }\:OC \,=\,r\,=\,\frac{d}{2},\;AD \,=\,y,\;DC\,=\,x.$

$\text{Consider right triangle CDO:}$
Code:
          x
D * - - - * C
|     *
r-y |   * r
| *
*
O
$\text{Pythagoras says: }\:x^2\,+\,(r\,-\,y)^2 \:=\:r^2 \;\;\;\Rightarrow\;\;\;x^2\,+\,r^2\,-\,2ry\,+\,y^2 \:=\:r^2$

[color=beige]. . . . . [/color]$x^2\:=\:2ry\,-\,y^2 \;\;\;\Rightarrow\;\;\;x \:=\:\sqrt{2ry\,-\,y^2}$

Last edited by skipjack; July 31st, 2015 at 10:59 PM.

 July 24th, 2013, 12:50 AM #3 Newbie   Joined: Jul 2013 Posts: 2 Thanks: 0 Re: Looking for a formula to calculate a chord length Beautiful. Works a treat thank you, that's much appreciated.

 Tags calculate, chord, formula, length

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