Posted by **Dylan** on Friday, May 6, 2011 at 11:45am.

The radius of a circle is 6cm and the arc measurement is 120 degrees, what is the length of the chord connecting the radii of the arc?

- geometry -
**Anonymous**, Friday, May 6, 2011 at 12:47pm
The ratio of a circle's circumference to its radius is 2ð

C=2rð

120°/360°=1/3

The length of the chord connecting the radii of the arc:

L=2rð/3

L=2*6*3.14159/3=37.69908/3= 12.56636 cm

- geometry -
**Anonymous**, Friday, May 6, 2011 at 12:47pm
ð=pi number

- geometry -
**Reiny**, Friday, May 6, 2011 at 3:37pm
The answer given by "anonymous" cannot be correct.

How can the chord be longer than the diameter, which would be only 12 cm ?

Draw an altitude from the centre to the chord creating two right-angled triangles with angles 30, 60 and 90°

If x is half of the chord

cos 30° = x/6

x = 6cos30 = 6√3/2 = 5.196

so the chord is 2(5.196) = 10.392

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