Two Circles With Inner Contact, Point Inside The Circles

Steps

1. Draw a circle e centred at A and passing through S0
2. Represent the given circles and the given point A through the circular inversion. This will be displayed at infinity
3. Draw the tangent of the circles
4. We display this tangent back through the circular inversion

Steps

0. Given are the circles a and b, which are touching internally. The point of tangency between them is D. Also given is the point A inside both circles.
1. Draw the line c that goes through the centres of a and b and intersects them in the point D.
2. Construct the perpendicular bisector of AD. It intersects c in the point S.
3. Draw the circle k that originates in S and has |SA| as its radius. It is the only solution.