$(15$ Points$)$ A proposed highway has two tangents of bearings $N45{54}^{\text{'}}{36}^{\text{'}\text{'}}E$ and $N1{22}^{\text{'}}$

$30"$ 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 is to be $43\mathrm{.}00ft.$ The PI is at

station $65+43\mathrm{.}21.$

Determine:

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

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

$($c$)$ The length of the tangent of the curve

$($d$)$ The length of the curve

$($e$)$ The stationing of the PC and the PT