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!

 

 

 

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