Triangle DEF is inscribed in circle G. In circle G, angle EDF=29 and arc DF has a measure of 132. If the circumference of circle G is 24 units, what is the length of arc DE? Express your answer as a common fraction.

Answer 1

First, we need to find the measure of arc DE.

Since angle EDF is inscribed in a circle, we know that the measure of the central angle subtended by arc DF is double the measure of angle EDF. Therefore, the central angle for arc DF is 29 x 2 = 58 degrees.

Since the circumference of the circle is 24 units and the central angle for arc DF is 58 degrees, we can use the formula for the circumference of a circle to find the radius of circle G.

C = 2πr
24 = 2πr
r = 12/π

Now, we can use the formula for the length of an arc, given by:

Length of arc = (central angle/360) * circumference

For arc DE, the central angle is 360 - 132 - 58 = 170 degrees.

Length of arc DE = (170/360) * 2π(12/π)
Length of arc DE = (17/36) * 24
Length of arc DE = 8/3 units

Therefore, the length of arc DE is 8/3 units.