Question #$1$: Horizontal Curve Design $|2$ pts

A proposed highway $($circular$)$ curve with a $50-mph$ design speed and radius of $1100ft$ will have an atgrade crossing with an existing railroad line at point $A$ as shown in the figure below. The railroad is parallel to the line connecting the PI to the PT and the separation distance is $150ft.$ The station of the PI is $96+56.$ Find the station of Point A$.($Note: the figure is drawn proportionally$).$ Hints: $(1)$ Notice the angle between the tangent lines and the curve radii at the PC and the PT$.(2)$ How can we find the arc length between points A and PT$?$