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The line joining the points A(0,5) and B(4,1) is a tangent to a circle whose centre C is at the point (4,4). Find
(i) the equation of the line AB.
(ii) the equation of the line through C which is perpendicular to the line AB.
(iii) the coordinates of the point of contact of tangent line AB with the circle.

Answer:
(i) The equation of the line AB is .
(ii) The equation of the line through C which is perpendicular to the line AB is .
(iii) The coordinates of the point of contact of tangent line AB with the circle is