Multiple choice

An arc of (60^o) in one circle is double the arc in a second circle whose radius is three times that of the first circle. What is the degree measure of the arc of the second circle?

  1. $\(30^o\)$
  2. $\(20^o\)$
  3. $\(10^o\)$
  4. $\(15^o\)$
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C Correct answer
Explanation

Arc length = radius × angle (in radians). Let first circle have radius r and angle 60°. Its arc length = r × 60°. Second circle has radius 3r and unknown angle θ. Its arc length = 3r × θ. Given that first arc is double the second: r × 60° = 2(3r × θ). Solving: 60° = 6θ, so θ = 10°.

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