Question 1
Given a triangle $ABC$ and a point $P_0$ on the side $AB$. Construct points $P_i$, $Q_i$, $R_i$ as follows: $Q_i$ is the foot of the perpendicular from $P_i$ to $BC$, $R_i$ is the foot of the perpendicular from $Q_i$ to $AC$ and $P_i$ is the foot of the perpendicular from $R_{i-1}$ to $AB$. Show that the points $P_i$ converge to a point $P$ on $AB$ and show how to construct $P$.