TITLE: Question about property of circle
QUESTION [0 upvotes]: We know that equal chords are equidistant from the center.
However, I was curious if the lengths involved are proportional as well since the circle is a pretty symmetrical shape. Here's what I mean: 
Let there be two chords,C1 and C2, in a circle at distances D1 and D2 from the center. Will  L1 and L2 be proportional to the distances D1 and D2?  
Is   $  \frac{L1}{L2} = \frac{D1}{D2} $ true?

REPLY [1 votes]: rUse pythagoras with $R$ as the radius of the circle
$R^2=D_1^2+\left(\cfrac{L_1}2\right)^2=D_2^2+\left(\cfrac{L_2}2\right)^2$
or you can use trigonometric functions of half the angle subtended by the chord at the centre of the circle, which amounts to the same thing. So it isn't quite as neat as you conjectured, Note that the chord gets shorted as the distance from the centre increases. It is zero when the distance is equal to the radius.
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