Using the given information, the length of arc EF in circle C is 9.75
Calculating the length of an arc
From the question, we are to calculate the length of arc EF
First, we will determine the measure of angle BAD
Let angle BAD = θ
From the question,
Length of arc BD = 6.5
Radius of circle A = 4
Using the formua,
[tex]Length \ of \ an \ arc = \frac{\theta}{360 ^\circ}\times 2\pi r[/tex]
Then,
[tex]6.5 = \frac{\theta}{360 ^\circ} \times 2\pi \times 4[/tex]
[tex]\theta = \frac{360 \times 6.5}{2\pi \times 4}[/tex]
[tex]\theta = \frac{2340}{8\pi }[/tex]
[tex]\theta = \frac{292.5}{\pi }^\circ[/tex]
Now, for the measure of arc EF in circle C
Since angle ECF and angle BAD are congruent, then
Angle ECF = [tex]\frac{292.5}{\pi }^\circ[/tex]
Thus,
Length of arc EF = [tex]\frac{\frac{292.5}{\pi}^\circ }{360 ^\circ} \times 2 \pi \times 6\\[/tex]
Length of arc EF = [tex]\frac{292.5^\circ }{\pi \times 360 ^\circ} \times 12 \pi[/tex]
Length of arc EF = [tex]\frac{292.5 \times 12}{360}[/tex]
Length of arc EF = 9.75
Hence, using the given information, the length of arc EF in circle C is 9.75
Learn more on Calculating the length of an arc here: https://brainly.com/question/12152333
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