If the radius of the circle becomes three times of the original, and the length of the opposite arc remains the same, the central angle of the arc is the same as that of the original arc______ Times

If the radius of the circle becomes three times of the original, and the length of the opposite arc remains the same, the central angle of the arc is the same as that of the original arc______ Times

Let the radius of the original circle be r, the arc length be l, and the center angle of the changed circle be x, then the center angle of the original arc is 180L π R, then l = x π· 3r180. The solution is: x = 60L π R, and the center angle of the arc is 13 times that of the original arc, so the answer is: 13

Let R be the radius of the circle, then the center angle of the arc with 34R is______ ．

According to the arc length formula: θ = LR = 34rr = 34, R is the radius of the circle, then the center angle of the arc with arc length of 34R is 34