Construct the following diagram in which the circles and lines intersect tangentially.
I created two circles (larger circles. Next, I constructed the segment connecting their centers. Then, I constructed the intersection points of the segment and the circles. I then constructed another segment connecting these two intersection points and the midpoint of this segment. I constructed a perpendicular line going through the midpoint and perpendicular to the segment. I then constructed two circles with a radius of 1.5 and two circles with a radius of .5. This gave me the above construction. I could not figure out how to make the two smaller circles tangent to the original larger circles.