Given: Two line segments a and c where c < a/2.

Show that there exists a segment of length b that can lead to the following
construction.

Part of the construction is to show that there exists a line through the
center of both the circles

of radius a and b and is tangent to the circle of radius c. All three circles
must be tangent to the

base line, then circles with radii a and c must be tangent as well as the
circles of radii b and c.

To this extent we found at least two different constructions.

The first of which involved starting from the radius c and working outward
from there.

click here for the first GSP construction.

The second construction we started with the radius of a and expanded our
construction to the right.

click here for the second GSP construction.

There does exist at least three other construction that demonstrate this
particular problem that

have been achieved by our fellow students.

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