a quadrilateral & the point X

There is quadrilateral ABCD. Point P is the center of gravity of triangle ABC. Point Q is the center of gravity of triangle ACD.Point R is the center of gravity of triangle ABD.Point S is the center of gravity of triangle BCD.

Segmets PQ and the RS cross at point X.
What is point X of the quadrilateral?

When point X is consistent with P or Q or R or S, what is the shape of the quadrilateral ?

When point X is consistent with point of intersection AC and BD, what is the shape of the quadrilateral ?


@You can also move points A, B, C, D on CABRI.

Download CABRIU data (d23) from here.