Consider a circle with center $O$ and radius $r$, and a tangent $t$ at point $A$ of the circle. Let $M$ be a point on the tangent $t$. The intersection point of segment $OM$ with the circle is denoted by $N$. In point $M$, we measure the distance $MP = MN$ on the perpendicular to $t$ raised at $M$, for example, on the side of $t$ where the circle is not located. What is the geometric locus of point $P$ as $M$ moves along the tangent $t$?