Two concentric clrcles are intercepted by the same central angle. the resulting arc length of the larger circle is 16 m and the radius ofthe larger crcle is 12 m. the radius of the smaller circle corresponding arc ofthe smaller. what’s the length of the corresponding arc of the smaller circle in meters (m)?

The correct question in the attached figure

Let
A°-----------> the same central angle

For the larger circle
length of larger circle=2*pi*r-------> 2*pi*12-----> 75.36 m

if 360° (full circle) has a length of------------> 75.36 m  
A°-----------------------------------> 16 m
A°=(16)*360/75.36--------> A=76.43°

For the smaller circle
length of smaller circle=2pi*r-------> 2*pi*7.5-----> 47.1 m

if 360° (full circle) has a length of------------> 47.1 m  
76.43°-----------------------------------> X
X=76.43*47.1/360-----> X=10 m ----> length arc of the smaller circle

the answer is
the length arc of the smaller circle is 10 m