Problem $1(20$ pts$)$ A proposed highway has two tangents of bearings $N71{54}^{\text{'}}{36}^{\text{'}\text{'}}E$ and $N52{22}^{\text{'}}{38}^{\text{'}\text{'}}W.$ The highway design engineer, attempting to obtain the best fit for the simple circular curve to join these tangents, decides that the external ordinate $($E$)$ is to be $78\mathrm{.}00ft.$ The PI is at station $65+44.$

Determine:

$($a$)$ The external angle of the curve $()$

$($b$)$ The radius of the curve

$($d$)$ The station of the PC

$($f$)$ The station of the PT