Two Circles With Inner Contact, Point Inside The Circles

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.

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