4.18. Three points $A, B$, and $C$ on a sphere of radius $R$ are connected pairwise (by the shorter) arcs of great circles. Another great circle is drawn through the midpoints of the arcs $A B$ and $A C$, intersecting the extension of the arc $B C$ at point $K$. Find the length of the arc $C K$, if the length of the arc $B C$ is $l(l<\pi R)$. (A great circle is the section of a sphere by a plane passing through its center.)
4.18. The plane passing through the center of the sphere and the midpoints of the chords $A B$ and $A C$ also passes through the midpoints of the chords $A B$ and $A C$, and is therefore parallel to the chord $B C$. Consequently, the great circle passing through $B$ and $C$, and the great circle passing through the midpoints of the arcs $A B$ and $A C$, intersect at two points $K$ and $K_{1}$ such that the diameter $K K_{1}$ is parallel to $B C$. Therefore, the length of the arc $C K$ is $(\pi R \pm l) / 2$.