$(50$ pts$)$ A horizontal curve is designed for a two$-$lane road given an intersection angle of $250.$ The station of the PC is at $2494+30\mathrm{.}5$ and the middle ordinate, $M,$ is $64\mathrm{.}15ft.$ Determine the following:

$($a$)$ Radius of the curve

$($b$)$ Station of the PT

$($c$)$ Deflection angle and chord length to the first even $100ft$ station.

$($d$)$ Deflection angle and chord length to the second even $100ft$ station.

$($e$)$ Deflection angle and chord length to the last even $100ft$ station.