Try writing a proportion: (arc length)/(circumference) = (central angle)/(360). You know the circumference and the central angle; which part is missing?

Simplify $135/360$ before multiplying by 32. Can you divide both numbers by the same factor to get a simple fraction?

In Desmos, type the expression (135/360)*32 to represent the fraction of the circumference for a $135^\circ$ arc.

Look at the numerical result that Desmos gives for (135/360)*32; that value is the length of minor arc AB.

For any circle, the arc length is proportional to the central angle:

Here, we want the length of minor arc $AB$, and we know:

• Central angle $AOB = 135^\circ$
• Circumference $= 32$.

Compute what fraction of the full $360^\circ$ circle the $135^\circ$ angle represents:

Now simplify this fraction by dividing numerator and denominator by 45:

So the minor arc AB is $3/8$ of the entire circumference.

Use the proportion from Step 1 with the fraction from Step 2:

Now multiply $32$ by $3/8$:

• First, $32 \div 8 = 4$
• Then, $4 \times 3 = 12$

So the length of minor arc $AB$ is 12.