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A square is inscribed in the circle x2 +y2 -10x-6y+30=0.One side of the square is parallel to the liney=x+3,then one vertex of the square is
radius of circle = 2 = half of diagonal of square
therefore perpendicular distance of center of circle(5,3) from side of square=√2
equation of one side of square : y=x+k
by distance formula,
|5+k-3|/√2=√2
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)
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