MathNet 2009-part-01 — 175 problems (EN–VI) Question 98

Let $X$ be an interior point of $\triangle ABC$ and $S_1 = S_{XBC}$, $S_2 = S_{XCA}$, $S_3 = S_{XAB}$. Find the minimal area of a convex polygon, containing three segments equal and parallel to $XA$, $XB$, $XC$.