CONO-SUR 1999 Problem 2

Let $ABC$ be a triangle right in $A$ . Construct a point $P$ on the hypotenuse $BC$ such that if $Q$ is the foot of the perpendicular drawn from $P$ to side $AC$ , then the area of the square of side $PQ$ is equal to the area of the rectangle of sides $PB$ and $PC$ . Show construction steps.