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Two arcs of two different circles are of equal lengths. If these arcs subtend angles of 30° and 60° at the centers of their respective circles, find the ratio of the radii of the two circles.
  • a)
    2 : 1
  • b)
    5 : 2
  • c)
    3 : 4
  • d)
    2 : 7
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Two arcs of two different circles are of equal lengths. If these arcs ...
As per the given data
Converting the degree into radians
⇒ 30° = π/6 rad and 60° = π/3 rad
Let rand r2 be the radii of the two circles and l be the length of the each arc
We know that l = r θ
⇒ r1θ1 = r2θ2
⇒ r1/r2 = θ21
⇒ r1/r2 = (π/3)/(π/6)
⇒ r1/r2 = 6/3 = 2/1
∴ the required ratio = 2 : 1
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Most Upvoted Answer
Two arcs of two different circles are of equal lengths. If these arcs ...
Let the radius of the first circle be r1 and the radius of the second circle be r2.

The length of an arc is given by the formula: arc length = (angle/360) * 2πr.

For the first circle, the arc length is (30/360) * 2πr1 = πr1/6.
For the second circle, the arc length is (30/360) * 2πr2 = πr2/6.

Since the lengths of the two arcs are equal, we have the equation: πr1/6 = πr2/6.

Dividing both sides of the equation by π/6, we get: r1 = r2.

Therefore, the radii of the two circles are equal.
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Two arcs of two different circles are of equal lengths. If these arcs subtend angles of 30° and 60° at the centers of their respective circles, find the ratio of the radii of the two circles.a)2 : 1b)5 : 2c)3 : 4d)2 : 7Correct answer is option 'A'. Can you explain this answer?
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