calculating various cuts of a circle

Question

im trying to find some sort of formula to calculate lines within a circle.

I need to find the length of the various lines within the circle from which I only know the diameter. Is there some sort of formula that uses the dropoff of a circles side from the center?

Thanks, Martijn

Answer 1

If $h$ is the distance of the line from the center and $r$ the radius of the circle, the length of the line is given by: $$l=2\sqrt{r^2-h^2}$$

Answer 2

There are 2 equations to find the chord length of a circle depending on the information given (ie, the things that you know about the circle)

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1) Given the radius and central angle:

$$l = 2\cdot r\cdot sin(\theta / 2)$$

where r is the radius of the circle
and $\theta$ is the angle subtended at the center by the chord
Use this formula if you know the radius and central angle of the circle.

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2) Given the radius and distance to center:

$$l = 2\cdot\sqrt {r^{2} - h^{2}}$$

where r is the radius of the circle
and h is the perpendicular distance from the chord to the circle center
This is a formula for the length of a chord if you know the radius and the perpendicular distance from the chord to the circle center.
This formula is the result of a simple application of Pythagoras' Theorem.

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