Problem $3(25$ points$).$ A horizontal curve has the following properties: initial tangent bearing

$40{30}^{\text{'}}NE,$ final tangent bearing $49{30}^{\text{'}}SE,$ degree of the curve is $5$ and station of $PC=10+00.$

Draw a sketch of the curve and determine the following:

$($a$)$ Radius of the curve.

$($b$)$ Length of the curve.

$($c$)$ Length of the main chord from PC to PT$.$

$($d$)$ Length of the minor chord from PC to a station $=11+00$ on the curve.

Use AASHTO GEOMETRIC DESIGN GUIDE.