Question 132
Dante's house is located in the $D$ point at the foot of a conical mountain with the base diameter of $4~\mathrm{km}$ and top at point $C$. It is known that $D$ is from $C$ $4~\mathrm{km}$ in a straight line and that, called $P$ the diametrically opposite point to $D$ Compared to the base of the mountain, the gateway to Hell is located at $3/4$ of the $CP$ segment, closer to $P$. What distance should Dante travel to a minimum (walking on the slopes of the mountain) to be able to reach the door of Hell from his home?