Multiple choice

In two circles, arcs of same length subtend angles of 60° and 90° at the centres. Find the ratio of their radii.

  1. 60 : 70

  2. 2 : 3

  3. 3 : 2

  4. None of these
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C Correct answer
Explanation

Arc length s = r * theta (in radians). Since arc lengths are equal, r1 * theta1 = r2 * theta2. Thus r1/r2 = theta2/theta1 = 90/60 = 3/2.

AI explanation

Using the arc length formula, arc length equals radius multiplied by the angle in radians. Since the arc lengths are equal, radius one multiplied by 60 degrees equals radius two multiplied by 90 degrees. Converting to a ratio gives radius one divided by radius two equals 90 divided by 60, which simplifies to a ratio of 3 is to 2.

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