Tangent Circles to a Circle and a Line

By Thuy Nguyen

__Construction__:

1. Begin with a circle center at K and a line L. Choose P to be an arbitrary point on the circle.

2. Construct a line M that passes through the center of the circle and the point P and then a line N that is perpendicular to line M.

3. Construct the intersection point of line L and line N, call x. Then bisect <pxy and <pxz.

4. One of the tangent circles will be centered at one of the intersection points of one angle bisector with M and radius is from that point to P, and the other tangent circle will be centered at the other intersection point of the other angle bisector with M and radius is from that point to P.

__Observations__:

1. The original circle is always contained in one of the tangent circles.

2. The two tangent circles are actually tangent to each other!