Question 190347
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The length of a chord given the perpendicular distance of the chord from the center of the circle, <i><b>d</b></i>, and the radius of the circle, <i><b>r</b></i>, is given by:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  L_c\ =\ 2 \sqrt{r^2 - d^2}]


Which is a simple application of Pythagoras' Theorem - see illustration:



{{{drawing(
500, 500, -10, 10, -10, 10,

circle(0,0,9),
blue(line(0,0,0,7)),
blue(line(.02,0,.02,7)),
blue(line(-.02,0,-.02,7)),
blue(line(0,0,5.6585,7)),
green(line(-5.6585,7,5.6585,7)),
locate(3,2.5,r=9),
locate(0.5,5,d=7),
locate(2.5,8.5,half_chord= sqrt(r^2-d^2))
)}}}


So,


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  L_c\ =\ 2 \sqrt{9^2 - 7^2}]


You can do your own arithmetic.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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