Question 25
Let $M$ be arbitrary point inside triangle $ABC$. Lines $AM$, $BM$, $CM$ intersect circumcircle of the triangle $ABC$ at points $D$, $E$, $F$ respectively. Denote $O_1$, $O_2$, $O_3$ centres of circumcircles of triangles $BCM$, $CAM$, $ABM$ respectively. Show that lines $DO_1$, $EO_2$, $FO_3$ pass through a point.
