Tangent Circles to a Circle and a Line
By Thuy Nguyen
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.
1. The original circle is always contained in one of the tangent circles.
2. The two tangent circles are actually tangent to each other!