*Constructing
a Circle Tangent to a Given Line *

*and a Given
Circle*

*by Amy Benson*

**We begin with a given circle and a
given line, such as**

**The task at hand in to construct a
circle that is tangent to both of the givens at the same time.
First, construct a line parallel to the given line through the
center of the given circle. **

**Next, construct a line perpendicular
to these two lines through the center of the circle. **

**Construct a point of intersection between
the perpendicular and the given circle as well as the point of
intersection between the perpendicular and the given line. **

**Construct a segment between these two
points of intersection. **

**Construct the midpoint of this segment
(this is the center of the tangent circle). **

**Construct the circle with this center
and a point on the circle being one of the points of intersection.
**

**To see the effects of changing one
or both of the givens and to confirm that the constructed (red)
circle does indeed remain tangent to both the given line and the
given circle at all times, click
here. To use a script of this construction with your own given
circle and line, click here.**

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Benson's Homepage**