Two triangles $ACE, BDF$ are given which intersect at six points: $G, H, I, J, K, L$ as in the picture. It is known that in each of the quadrilaterals \[ABIK ,BCJL ,CDKG ,DELH ,EFGI\]it is possible to inscribe a circle. Is it possible for the quadrilateral $FAHJ$ is also circumscribed around a circle?
Attachments:
