Appolonius # 5


Case 1 : Two intersecting lines and a point.

Click here for a GSP sketch where you can move the lines and point.


Construction:

Given lines AF and CF, point E.

Steps:

1. Construct angle bisector FY.
2. Construct any circle (G) tangent to the two lines.
3. Draw line FE and mark points of intersection with circle G.
4. Draw radii of circle G at points of intersection and construct lines
parallel to radii at point E. Mark points of intersection with angle
bisector FE (centers of the tangent circles).
5. Construct circles from each center through point E.

Case 2 : Two parallel lines and a point.