Given two
circles and a point on one of the circles. Construct a circle tangent
to the two circles with one point of tangency being the designated
point.
Start by constructing a
circle. Label the center A. Now construct a second circle
inside this first circle. Label the center of the second circle B.
Hide the points used to make
the radius of the circle, so as to avoid confusion later. Put
arbitrary points on the smaller and larger circle and label them C and
D respectively. Point D will be the point at which the
tangent circle we are about to construct will be tangent to Circle A.
Construct a line through Point A and
Point D. The radius of our tangent circle will lie on segment
AD.
Construct segment BC.
Use this segment to construct a circle centered on Point D with radius
length BC.
Construct
a line segment that has Point B as one endpoint, and the intersection
of line AD and Circle D as the other endpoint.
Construct the perpendicular
bisector of line BD. The radius of our tangent circle will be the
length of the segment DG. (G is shown labeled in the next
figure.) This tangent circle will be centered on Point G.
Use these two pieces of information to construct the tangent circle.
The
final step to clean up the picture is to hide the lines and circles we
used to construct our tangent circle. You should be left with the
original circles (with their centers) and the tangent circle with
center G.
