Assignment
7

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.

Answer:

LetŐs
start with one large circle with center A and construct a smaller circle inside
the larger circle, center B.

Then,
place an arbitrary point on each circle, C and D respectively.

Next,
construct a line segment from point B to point C, this will be the radius of a
circle with center D; additionally, create a line that goes through points A
and D.

Then,
use the line segment BC to create a like circle with center D.

Next,
label a point, E, lying on the newly constructed circle and also on the new
line.

Then,
construct a line segment from point B to point E and label the midpoint F.

Next,
construct a line perpendicular to segment BE that passes through point F. This
line passes through line AD at newly labeled point, G.

Finally,
create a circle with a radius equal to the length of GD which creates our
circle that is tangent to the two other circles.