KöMaL 2008 B4126

From the endpoints of a chord $AB$ of a circle, drop perpendiculars onto a tangent drawn at a point $P$ of the circle, different from $A$ and $B$. Drop a perpendicular from $P$ onto the chord $AB$. Prove that the perpendicular dropped onto the chord is the geometric mean of the perpendiculars dropped onto the tangent.