Find The Radical Centre Of Circles x2 + y2 + 3x + 2y + 1 = 0, X2 + y2 – x + 6y + 5 = 0 And x2 + y2 + 5x – 8y + 15 = 0. Also Find The Equation Of The Circle Cutting Them Orthogonally.

Examine if the two circles x² + y² – 2x – 4y = 0 and x² + y² – 8y – 4 = 0 touch each other externally or internally.

Find the equation of the circle passing through (1, 1) and the points of intersection of the circles

x² + y² + 13x – 3y = 0 and 2x² + 2y² + 4x – 7y – 25 = 0.

Find the equation of the circle passing through the point of intersection of the circles x² + y² – 6x + 2y + 4 = 0, x² + y² + 2x – 4y – 6 = 0 and with its centre on the line y = x.

Find the equation of the circle passing through the points of intersection of the circles x² + y² – 2x – 4y – 4 = 0 and x² + y² – 10x – 12y + 40 = 0 and whose radius is 4.

Find the equation of the circle through points of intersection of the circlex² + y² – 2x – 4y + 4 = 0 and the line x + 2y = 4 which touches the line x+ 2y = 0.

Find the circle whose diameter is the common chord of the circles x² + y²+ 2x + 3y + 1 = 0 and x² + y² + 4x + 3y + 2 = 0.

Find the angle between the circles

Find the equation of the circle which cuts the circle x² + y² + 5x + 7y – 4 = 0 orthogonally, has its centre on the line x = 2 and passes through the point (4, –1).

Find the equations of the two circles which intersect the circles

        x² + y² – 6y + 1 = 0 and x² + y² – 4y + 1 = 0  

Orthogonally and touch the line 3x + 4y + 5 = 0.   

Find the radical centre of three circles described on the three sides 4x – 7y + 10 = 0, x + y – 5 = 0 and 7x + 4y – 15 = 0 of a triangle as diameters.