Problemas de desafío: longitud de arco (radianes) 1

$\begin{array}{rl}\text{Circunferencia}& =2\pi r\\ & =2\pi (25)\\ & =50\pi \end{array}$‍

$\text{m}\stackrel{⌢}{BCA}=2\pi -{\displaystyle \frac{3}{10}}\pi$‍

$\begin{array}{rl}{\displaystyle \frac{\text{longitud del arco}}{\text{circunferencia}}}& ={\displaystyle \frac{\text{medida del arco}}{\text{radianes en un círculo}}}\\ \\ \\ {\displaystyle \frac{\text{longitud del arco}}{50\pi }}& ={\displaystyle \frac{\left({\displaystyle \frac{17}{10}}\pi \right)}{2\pi }}\\ \\ \\ \text{longitud del arco}& ={\displaystyle \frac{17}{10}}\pi \cdot {\displaystyle \frac{50\pi }{2\pi }}\\ \\ \\ & ={\displaystyle \frac{85}{2}}\pi \end{array}$‍

$\begin{array}{rl}\text{Circunferencia}& =2\pi r\\ & =2\pi (10)\\ & =20\pi \end{array}$‍

$\begin{array}{rl}\text{m}\mathrm{\angle }APE& =\text{m}\mathrm{\angle }BPD\\ {\displaystyle \frac{19}{36}}\pi & ={\displaystyle \frac{\pi }{3}}+\text{m}\mathrm{\angle }CPD\\ {\displaystyle \frac{7}{36}}\pi & =\text{m}\mathrm{\angle }CPD\end{array}$‍

$\begin{array}{rl}{\displaystyle \frac{\text{longitud del arco}}{\text{circunferencia}}}& ={\displaystyle \frac{\text{medida del arco}}{\text{radianes en un círculo}}}\\ \\ \\ {\displaystyle \frac{\text{longitud del arco}}{20\pi }}& ={\displaystyle \frac{\left({\displaystyle \frac{7}{36}}\pi \right)}{2\pi }}\\ \\ \\ \text{longitud del arco}& ={\displaystyle \frac{7}{36}}\pi \cdot {\displaystyle \frac{20\pi }{2\pi }}\\ \\ \\ & ={\displaystyle \frac{35}{18}}\pi \end{array}$‍