A square is inscribed in the circle x² +y² -10x-6y+30=0.One side of the square is parallel to the line y=x+3.Find the vertices of the square.

radius of circle = 2 = half of diagonal of square therefore perpendicular distance of center of circle(5,3) from side of square=v2 equation of one side of square : y=x+k by distance formula, |5+k-3|/v2=v2 k=0,-4 the two side of square are: y=x and y=x-4 solving the lines with the equation of circle, we get: vertices: (3,3),(5,5),(5,1),(7,3)