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

1. 
 Start with the given circle, and determine the center of the tangent circle (inside 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 near 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 near side.

