OBM 1980 Problem 3

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 $P$ .