Question 103
For a triangular pyramid $OABC$,
$OA = 2$, $OB = 3$, $OC = 4$, $\angle AOB = \angle BOC = \angle COA$
are satisfied. Furthermore, there is a point $X$ on the base $ABC$ for which
$\angle AOX = \angle BOX = \angle COX = 30^\circ$.
Determine the volume of this triangular pyramid $OABC$. Here, by $PQ$ we denote the length of the line segment $PQ$.
$OA = 2$, $OB = 3$, $OC = 4$, $\angle AOB = \angle BOC = \angle COA$
are satisfied. Furthermore, there is a point $X$ on the base $ABC$ for which
$\angle AOX = \angle BOX = \angle COX = 30^\circ$.
Determine the volume of this triangular pyramid $OABC$. Here, by $PQ$ we denote the length of the line segment $PQ$.