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Answer :
Final answer:
To find the ratio between the radii of the two circles, we can use the fact that the ratio between the arc lengths is equal to the ratio between the radii. The ratio between the radii of the two circles is 1:6 or 1/6.
Explanation:
To find the ratio between the radii of the two circles, we can use the fact that the ratio between the arc lengths is equal to the ratio between the radii. Let's assume the radius of the circle with the 60 degree central angle is r1, and the radius of the circle with the 80 degree central angle is r2.
We know that the arc length opposite to the 60 degree central angle is equal to the arc length opposite to the 80 degree central angle. Since the circumference of a circle is directly proportional to its radius, we can set up the following equation:
60/360 = r1/r2
Simplifying this equation, we get 1/6 = r1/r2. Cross-multiplying, we find that r1 = (1/6) * r2.
Therefore, the ratio between the radii of the two circles is 1/6, which can be written as 1:6 or 1/6.
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