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KCET2024MathematicsCircle

If in two circles, arcs of the same length subtend angles 30^ and 78^ at the centre, then the ratio of their radii is

Options

  1. A5 13
  2. B13 5
  3. C13 4
  4. D4 13

Correct answer

B. 13 5

Step-by-step solution

Let the radii of the two circles be r₁ and r₂ . Let an arc of length l subtend an angle of 30^ at the centre of the circle of radius r₁ , while let an arc of length l subtend an angle of 78^ at the centre of the circle of radius r₂ . Now, 30^ = 6 radian and 78^ = 13 30 radian We know that in a circle of radius r unit, if an arc of length l unit subtend an angle radian at the centre, then = l r or l=r l= r₁ 6 and l= r₂ 13 30 r₁ 6 = r₂ 13 30 r₁=r₂ 13 5 r₁ r₂ = 13 5

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