Two circles are concentric. Two arcs are formed by the same central angle, with arc lengths of 54 and 81 respectively. Which of the following are possible radii for the circles? Select the two correct answers.

Question

40 and 60

23 and 32

32 and 64

14 and 41

12 and 18

Answer 1

Angle = arc/radius
81/R1 = 54/R2
54 R1 = 81 R2
R1/R2 = 81/54 = 9*9 / 9*6 = 3*3*3*3 / 3*3*3*2 = 3/2
60/40 = 20*3 / 20*2 = 3/2 sure enough
now it's your turn( If you can not divide the big one by 3, it is no good.)