
How to construct a circle tangent to a given circle at the far side, from a center inside or on that circle?

1. 
 Start with the given circle, and determine the center of the tangent circle (inside or on the given circle).


2. 
 Draw the connecting line between the center of circle 1 and the given point (the center of the tangent circle to be constructed).


3. 
 Extend line 2 up to the far side of circle 1.


4. 
 Construct a circle centered at the given point (1), passing through the intersection of line 3 and circle 1.


5. 
 Circle 4 is the circle to be constructed. It has the given point as its center and is tangent to the given circle at the far side.

