Find the radius from a chord

Thanks Robert. Your suggestion solved my problem.

I have the Delta Angle and the Cord Length

I need the Radius

[JohnS]

Originally Posted by Unregistered

I have the Delta Angle and the Cord Length

I need the Radius

You have to use half the chord length and half the central angle

R = 0.5*c/sin(0.5*theta)

[maha]

please i would like to know how i can measure the radius knowing the length of the chord xz and the lenght of the arc??

[maha]

any one answer plzzzzzzzz

[JohnS]

Originally Posted by maha

please i would like to know how i can measure the radius knowing the length of the chord xz and the lenght of the arc??

see post #22

formula to find the length when given only the chord

I just had a great time solving this one. It's a fun one!
If the chord length is 2b, and the sagitta/height is s and the apothem (radius minus the height) is a and the radius is c, then pythagoras gives

(1) a^2+b^2=c^2
and since the radius is the sum of apothem and the sagitta:
(2) c=a+s

then solve pythagoras for b^2 and sub (2) into it
(3) b^2=(a+s)^2-a^2
(4) b^2=a^2+2as+s^2-a^2
(5) b^2=2as+s^2

solve for a:
(6) a=(b^2-s^2)/(2s)

sub (6) into (2)
(7) c=(b^2-s^2)/2s +s
(8) c= (b^2-s^2+2s^2)/2s
(9) c= (b^2+s^2)/(2s)

as long as you remember that b is HALF the chord length.

it is given that ab is the diameter of a circle and o is its centre. ab bisects the chord cd at e such that ce=ed= 8 cm and eb= 4cm. find the radius.

[alexuslara]

how about calculating the area of a segment when the only information available are the length of the cord and the hight of the segment? (in your figure it would be "C" and "M"). Thanks, Gabriel