### Instruction: Let $A,$ $B,$ and $C$ be points on a circle of radius $18.$ If $\angle ACB = 70^\circ,$ what is the circumference of the minor arc ${AB}$? Express your answer in terms of $\pi.$.### Response: I know that the measure of an arc is proportional to the central angle that subtends it, so I can use a proportion to find the circumference of the minor arc ${AB}.$
Let $x$ be the circumference of the minor arc ${AB}.$
Then I can write the proportion $\frac{x}{2\pi(18)} = \frac{70}{360}.$
I can cross-multiply and simplify to get $x = \frac{7}{18}\pi(18),$ or $x = 7\pi.$