THE TANGENCIES OF 



THE TEN PROBLEMS OF APOLLONIUS IN TIIE TANGENCIES OF CIRCLES. 



No. 1. 



To draw a circle through three points. Number of solutions, 



No. 2. 

 To draw a circle through two points, and tangent to a given 

 right line. Number of solutions, two. 



No. 3. 



To draw a circle through a point, and tangent to two right 

 lines. Number of solutions, two. 



No. 4. 

 To draw a circle through two points, and tangent to a given 

 circle. Number of solutions, two. 



No. 5. 



To draw a circle through a given point, and tangent to a given 

 right line, and to a given circle. Number of solutions, four. 



No. 6. 



To draw a circle through a given point, and tangent to two 

 given circles. Number of solutions, four. 



No. 1. 

 To draw a circle tangent to three given right lines, of which 

 not more than two are parallel. Number of solutions, four. 



No. 8. 



To draw a circle tangent to two right lines and a given circle. 

 Number of solutions, four. 



No. 9. 



To draw a circle tangent to a given right line and to two given 

 circles. Number of solutions, eight. 



No. 10. 



To draw a circle tangent to three given circles. Number of 

 solutions, eight. 



