A circle has center O , and points A and B lie on the circle. The

Choice D is correct. It’s given that the measure of arc $AB$ is $45°$ and the length of arc $AB$ is $3 \text{inches}$. The arc measure of the full circle is $360°$. If $x$ represents the circumference, in inches, of the circle, it follows that $\frac{45°}{360°}=\frac{3 \text{inches}}{x \text{inches}}$. This equation is equivalent to $\frac{45}{360}=\frac{3}{x}$, or $\frac{1}{8}=\frac{3}{x}$. Multiplying both sides of this equation by $8x$ yields $1\left(x\right)=3\left(8\right)$, or $x=24$. Therefore, the circumference of the circle is $24 \text{inches}$.

Choice A is incorrect. This is the length of arc $AB$.

Choice B is incorrect and may result from multiplying the length of arc $AB$ by $2$.

Choice C is incorrect and may result from squaring the length of arc $AB$.