Both Points Outside A Circle

Steps

1. Construct a circle for circular inversion. Choose the point A as its centre and the distance between the assigned points (the line segment AB) as its radius.
2. Invert the assigned circle into the newly constructed one with the help of circular inversion.
3. After constructing the new circle with c. inversion, construct its tangents which pass through the point B.
4. Construct two circles with the circular inversion of tangents of the circle constructed in the first step. The two circles, k1 and k2, are the solution.