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Two equal arcs of different circles C1 and C2 subtend angles of 600 and 750 respectively, at the centres. What is the ratio of the radius of C1 to the radius of C2 ?
4 : 5
5 : 4
1 : 1
3 : 2
- Two equal arcs mean the arc length is the same for both circles.
- Arc length = Radius × Angle in radians.
- Let \( r_1 \) be the radius of circle C1 and \( r_2 \) be the radius of circle C2.
- The angle at the center for C1 is 60 degrees, and for C2 is 75 degrees.
- Convert angles to radians: 60 degrees = \( \frac{\pi}{3} \), and 75 degrees = \( \frac{5\pi}{12} \).
- For equal arcs: \( r_1 \times \frac{\pi}{3} = r_2 \times \frac{5\pi}{12} \).
- Simplifying, we get \( \frac{r_1}{r_2} = \frac{5}{4} \).
- The correct option is 5:4.
By: Parvesh Mehta ProfileResourcesReport error
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