The coordinates of the middle point of the chord cut off by  2x−5y+18=0 on the circle x2+y2−6x+2y−54=0, are

The mid point is the intersection of the chord and perpendicular line on it from the centre (3, -1). The equation of the perpendicular line is 5x+2y-13=0. Therefore, the required point is  (1, 4).