the length of chord AB in D is 9mm. If the measure of angle AB is 32 then find the length of AB

The length of arc AB is 9.12 mm:

We first calculate for the radius r of the circle using the equation
     r = c/(2 sin[theta/2]) 

     where c is the length of chord AB that is given as 9 millimeters
                angle given is 32 degrees

To convert theta 32 degrees into radians:
     32 degrees * (pi/180) = 32 degrees * (3.14/180) = 0.5583 radians

We now substitute the values into the equation to find the radius r:
     r = 9/(2 sin[0.5583/2]) 
     r = 16.33 mm
.
We can finally solve for the length s of arc:
     s = r theta = 16.33 * 0.5583  = 9.12 mm