# geometry

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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 -

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 -

ð=pi number

• geometry -

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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