Both Points In A Circle, One Is The Centre

Steps

0. Given is the circle c, inside of which lie the points A and B. A lies in the centre of c
1. Construct the perpendicular bisector of AB, f. The resulting circles' origins will lie on it.
2. Construct a line parallel to f that goes through the point B, g. The points where g intersects c shall be named C and D
3. Construct the perpendicular bisectors of BC (h) and BD (i). The points where they intersect f shall be named F and E, respectively.
4. Draw the circles d and e:
5. d has E as its origin, goes through the points A and B, the point of tangency with c is D
6. e has F as its origin, goes through the points A and B, the point of tangency with c is C