Math Is Fun Forum

Dharshi

Member

Registered: 2006-10-31

Posts: 56

Radii??

Suppose arcs of same length in two circles subtend angles of 60degees and 75degrees  at the center. Find the ratio of their radii.

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Radii??

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 ratio

so the ratio of the radii is 1:4/5 = 5:4 (for circles with sectors of 60 and 75 respectively)

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