$(20$ points$)$ A horizontal curve is designed for a two$-$lane road in mountainous terrain. The following data are known:

Deflection angle: $80$ degrees

Tangent length: $600\mathrm{.}00$ feet

Station of PI: $1210+28\mathrm{.}84$;$fs=0\mathrm{.}12$;$e=0\mathrm{.}1$

Determine the following:

a$.$ Design speed in mi$/$h$.(6$ points$)$

b$.$ Station of the PC$.(6$ points$)$

c$.$ Station of the PT$.(6$ points$)$