Find the equation of a circle of radius 5 units which touches another circle `x^2 +y^2 - 2x - 4y - 20 = 0` at the point (5,5).

Find the equation of the circle whose radius is 5 and which touches the circle x^2 + y^2-2x- 4y- 20 = 0 externally at the point (5, 5).

Find the equation of a circle of radius 5 which lies within the circle x^2 + y^2+14x + 10y- 26 = 0 and which touches the given circle at the point (- 1, 3).

Find the equation of the circle concentric with the circle x^(2) + y^(2) - 8x + 6y -5 = 0 and passing through the point (-2, -7).

Find the equation of the circle through points of intersection of the circle x^2 + y^2 -2x - 4y + 4 =0 and the line x + 2y = 4 which touches the line x + 2y = 0 .

Find the equation of a circle concentric with the circle x^2 + y^2-2x -4y + 1 = 0 and whose radius is 5.

Find the equation of the circle passing through the points of intersection of the circles x^2 + y^2 - 2x - 4y - 4 = 0 and x^2 + y^2 - 10x - 12y +40 = 0 and whose radius is 4.

Find the equation of the circle which cuts orthogonally the circle x^2 + y^2 – 6x + 4y -3 = 0 ,passes through (3,0) and touches the axis of y.

Find the equation of the circle concentric with the circle x^2 + y^2+4x+ 6y+11=0 and Passing through the point (5, 4).

Find the equation of the circie concentric with the circle x^2 + y^2 + 4x-8y- 6 = 0 and having radius double of its radius.

Find the equation of the circle passing through the point of intersection of the circles x^2 + y^2 - 6x + 2y + 4 = 0, x^2 + y^2 + 2x - 4y -6 = 0 and with its centre on the line y = x.