MathNet 2017-part-07 — 172 problems (EN–VI) Question 24

Let $ABC$ be a triangle, and let $BCDE$, $CAFG$, $ABHI$ be squares that do not overlap the triangle with centers $X$, $Y$, $Z$ respectively. Given that $AX = 6$, $BY = 7$, and $CZ = 8$, find the area of triangle $XYZ$.