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Suppose arcs of same length in two circles subtend angles of 60degees and 75degrees at the center. Find the ratio of their radii.
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given the angle (in degrees) of a sector, the arc length will be
where a is the angle, and r the radius
for youre two arcs, you have to different angles, same arc length, thereby different radii
since were not told arc length, you cant find a value for r1 and r2, but you can get the ratio which is what the question wants
you can express r2 as a product of r1, so that you have
where k is the ratioso the ratio of the radii is 1:4/5 = 5:4 (for circles with sectors of 60 and 75 respectively)
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