A four$-$leg intersection with no traffic control is formed by two two$-$lane roads with the speed limits on the minor $(N-S)$ and the major $(E-W)$ being $40k\frac{m}{h}$ and $65k\frac{m}{h},$ respectively.

If a building is to be located at $15$ m from the centerline of the nearest lane on the minor road $(b$ in the figure$),$ determine the minimum distance at which the building could be located from the centerline of the outside lane of the major road $(a$ in the figure$)$ so that adequate sight distances are provided. Grades of all approaches are $0.$