The purpose of this assignment is to construct the tangent of two circles. First construct a larger circle. Then construct a smaller circle within the larger one. We will label these circle a and b, so that things will be clear later in the construction. Construct an arbitrary point c on the larger circle.

Now we will construct a line through the points a and c on the larger circle.

Construct segment from the b to c. Also construct a segment from the point b to an arbitrary point on that circle. Then construct a circle with the center point c and the same radius as circle b.

Now construct a segment from the point b to where the line ac intersect the circle with center point c. (This is the intersection on the farthest side of the circle) Then construct the midpoint of that segment.

Now construct a perpendicular line to the midpoint of the segment just created. Mark the intersection of the perpendicular line and the line ac.

Use the intersection just created to construct the tangent circle. This will be the center point of the circle. The radius will be from the intersection point to the point c.

Now hide the construction lines, segments, and circles to see a clearer picture of the tangent circle.