Construct the circle orthogonal to the given circle and pass

Construct the circle orthogonal to the given circle, and passing through the two given points Please list al SleRs B.

Solution

Let two points are A and B and given circle is c.

Let we have to construct a circle d.

(1) Given two points A and B and a circle c, then the center P of the circle d is the point of concurrence of the perpendicular bisector of AB, and the radical axes of A and c and of B and c.

(2) The radical axis of A and c can be constructed as the perpendicular bisector of AA\', where A\' is the inversion of A in c.

(3) The radical axis of B and c is constructed the same way from the inversion B\' of B in c.