# Find the radius of a circle from a chord

1. Feb 9, 2009

### Lizardjuice7

Hi,

Can someone please explain to me how you get the equation:

radius=($$\sqrt{c}$$+m2)/2m

c=length of chord

m=distance from midpoint of chord to edge of the circle

I would like to find the radius of the circle from only knowing those two quantities.

I have found the equation on various websites across the web (including http://www.math.utah.edu/~eyre/rsbfaq/physics.html), but I do not know how it was derived.

Thanks,

Lizardjuice7

2. Feb 9, 2009

### king vitamin

From the link you gave they say the equation is r = ((c^2)/4 + m^2)/(2m), which is very good because that's the answer i just got from solving the problem. (EDIT: I think I see the problem, the link gives c^2/4 without parenthesis so you probably assumed c^(2/4) instead of (c^2)/4)

Draw your circle with a chord and a line from the midpoint of the chord to the opposite side of the circle. Chord is of length c and line bisecting the chord is of length m.

Now draw a line connecting the midpoint of the circle (which is on line m) to one of the corners of the chord. Because line m bisects the chord, this is a right triangle.

Consider the angle theta between the chord and the origin (the angle on your triangle which does not on the origin). Using normal trig relations:

sin(theta) = (m - r)/r
cos(theta) = c/(2*r)

Now just compute sin(theta)^2 + cos(theta)^2 = 1 and do the algebra!

3. Feb 10, 2009

### Lizardjuice7

thanks, thats a big help