Question

Please answer step by step

Answer 1

The radii to the points of tangency in each circle are parallel. Connecting the tangent point of the smaller circle to the corresponding radius of the larger circle creates a right triangle with hypotenuse 16 +4+6 = 26 and leg 16 -6 = 10. These numbers let you find the straight length between wheels as
.. √(26^2 -10^2) = 24

The minor arc of belt around the smaller wheel is 2*arccos(10/26) = 2.35201 radians. Then the major arc of belt around the larger wheel is
.. 2π -2.35201 = 3.93117 . . . radians

Of course, the length of each arc is the product of radian measure and radius. Then the total belt length is
.. (16 cm)(3.93117 radians) +(6 cm)*(2.35201 radians) +2*(24 cm) = 125 cm