COLÉGIO NAVAL - CN 1982

[latex]\\\mathrm{Note\ que\ m\left (\widehat{RPS} \right )+\cancelto{90^{\circ}}{\mathrm{m\left (\widehat{PRC} \right )}}+\cancelto{120^{\circ}}{\mathrm{m\left (\widehat{RCS} \right )}} +\cancelto{90^{\circ}}{\mathrm{m\left (\widehat{CSP} \right )}}=360^{\circ}\ \therefore\ m\left (\widehat{RPS} \right )=60^{\circ}}\\\\ \mathrm{\ \ \ \ \ \ \ \ S=\frac{1}{2}\times \overline{PR}\times \overline{PS}\times sin\left ( \widehat{RPS} \right )=\frac{1}{2}\times R\times R\times sin\left ( 60^{\circ} \right )=\frac{1}{2}\times ( 8 )^2\times \frac{\sqrt{3}}{2}=16\sqrt{3}\ cm^2}[/latex]

muito obrigada!