A vertical curve connecting a rising gradient $1$:$50$ and a falling gradient $1$:$80$ is to be designed. The required sighting distance is $200m$ for a driver whose eye$-$level is $1\mathrm{.}05m$ from the road surface. If the chainage and reduced level of the highest point are $2532m$ and $100\mathrm{.}23m$ respectively, calculate :$-$

Chainage of the tangent points

$(8$ marks$)$

Design the curve at $20$ intervals

$(12$ marks$)$