Clearly the circle has (1,-2) as its centre and radius 21/2units.The sides of the square will be chords of the circle.Also the chords subtend a right angle at the centre of the circle.Radius of circle = r = 21/2units.Hence distance of side of square i.e distance of chord of circle that subtends a right angle at centre=r/21/2= 1 unit.As the side is parallel to the x-axis and y-axis,One side will be one unit to the right of the centre and one side will be one unit above the centre.Hence equations of two of the sides are x=2 and y=-1 respectively.The vertex of the square will be given by the point of intersection of these two lines.Hence the coordinates of one of the vertices is (2,-1).
