$(10$ points$)$ A horizontal curve has $=70{00}^{\text{'}}{00}^{\text{'}\text{'}},R=250\mathrm{.}00ft,$ and Station of $PC=[20+50\mathrm{.}00].$

a$.$ Tabulate all necessary data to stake the curve at full stations from PC to PT using either subdeflection method or tangent offset method.

b$.$ Determine the azimuth of chord from PC to PT given that the bearing of tangent from $PC$ to $\frac{?}{PI}$ is $N10{00}^{\text{'}}{00}^{\text{'}\text{'}}E.$

c$.$ Calculate the area enclosed by the curve and the two tangents $($keep $4$ significant figures$).$