A circle$\Gamma$ with radius $R$ and center $\omega$, and a line $d$ are drawn on a plane, such that the distance of $\omega$ from $d$ is greater than $R$. Two points $M$ and $N$ vary on $d$ so that the circle with diameter $MN$ is tangent to $\Gamma$. Prove that there is a point $P$ in the plane from which all the segments $MN$ are visible at a constant angle.