SAT Question c8345903: Circles answer and explanation with Desmos solution

Choice B is correct. The ratio of the lengths of two arcs of a circle is equal to the ratio of the measures of the central angles that subtend the arcs. It's given that arc $ADC$ is subtended by a central angle with measure $100^{\circ }$. Since the sum of the measures of the angles about a point is $360^{\circ }$, it follows that arc $ABC$ is subtended by a central angle with measure $360^{\circ }-100^{\circ }=260^{\circ }$. If $s$ is the length of arc $ABC$, then $s$ must satisfy the ratio $\frac{s}{5\pi }=\frac{260}{100}$. Reducing the fraction $\frac{260}{100}$ to its simplest form gives $\frac{13}{5}$. Therefore, $\frac{s}{5\pi }=\frac{13}{5}$. Multiplying both sides of $\frac{s}{5\pi }=\frac{13}{5}$ by $5\pi$ yields $s=13\pi$.