Problem

Source: 2021 Yasinsky Geometry Olympiad X-XI p6 , Ukraine

Tags: geometry, 3D geometry, sphere



Three lines were drawn through the point $X$ in space. These lines crossed some sphere at six points. It turned out that the distances from point $X$ to some five of them are equal to $2$ cm, $3$ cm, $4$ cm, $5$ cm, $6$ cm. What can be the distance from point $X$ to the sixth point? (Alexey Panasenko)