Multiple choice

In the circle above, segment $AB$ is a diameter. If the length of arc $\overline{ADB}$ is $8\pi $ , what is the length of the radius of the circle?

  1. $2$
  2. $4$
  3. $8$
  4. $16$
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C Correct answer
Explanation

Arc length of a semicircle is pi * r. Given arc ADB is 8*pi, and AB is diameter, the arc is a semicircle. pi * r = 8 * pi, so r = 8.

AI explanation

Segment AB is a diameter, so the arc ADB represents a semicircle with a central angle of 180 degrees. Using the circumference formula, the arc length of 8 times pi equals 180 divided by 360 times 2 times pi times the radius. Solving this equation gives the radius as 8.