Problem 631

$\checkmark$ Let's construct an equilateral triangle $ABC$ with side $AB$ and a circle centered at point $C$, passing through points $A$ and $B$. The arc $AB$ of this circle is seen from the center at an angle of $60^{\circ}$, and therefore from any point on the circle (lying on the same side of $AB$ as point $C$), the segment is seen at an angle of $30^{\circ}$. The same applies to the symmetric arc of the circle on the other side of $AB$. We obtain a figure consisting of two arcs of the circle, from any point of which the segment $AB$ is seen at an angle of $30^{\circ}$. As the previous problem shows, from points inside this figure, the segment $AB$ is seen at a larger angle, and from points outside it, at a smaller angle. $\triangleleft$

## A few more problems