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?

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

Find the length of the intercepted arc if the length of the central angle is 120 degrees and the radius of the circle is 6cm.

To find the length of the chord connecting the radii of the arc, we can use the formula:

Length of chord = 2 * Radius * sin(angle/2)

In this case, the radius of the circle is given as 6cm, and the arc measurement is given as 120 degrees. The angle (in degrees) should be converted to radians for trigonometric calculations.

First, let's convert the angle from degrees to radians:
Angle in radians = (Angle in degrees * π) / 180

Angle in radians = (120 * π) / 180
Angle in radians = (2 * π) / 3

Now, we can substitute the values into the formula to find the length of the chord:
Length of chord = 2 * Radius * sin(angle/2)
Length of chord = 2 * 6 * sin((2 * π) / 3)

Calculating the value of sin((2 * π) / 3), we get:
sin((2 * π) / 3) ≈ 0.866

Now we can substitute this value back into the formula to find the length of the chord:
Length of chord = 2 * 6 * 0.866
Length of chord ≈ 10.392 cm

Therefore, the length of the chord connecting the radii of the arc is approximately 10.392 cm.

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

ð=pi number