100.] TII rm 



23. (, i veo the two circles 



f i + j i -4x-2f + 40 and r + j i + 4* + 2jr-4oO; 

 find the equations of their common tangents. 



24. Kind the radical axis ,. les in example 23 ; show that it 

 it perpend tlie Hue joining the centers of the gi /en circles, and 



f the lengths of the segments into which the radical axis 



. joining the centers. How is this ratio related to the 



tie circles? Is this relation true for any pair of circles what- 



25 (.n, MI the three circlet: 





the jN.is.t from which tangents drawn to these three circles are of 

 equal length, also find that length. How is this point related in pc* 

 to the radical center of the giren circles? Prove that this relation is the 

 n.tMi" I'.T .inv tiutjfcafaisji 



26. Fin<l tlte locus of a point which moves so that the length of the 

 tangent, drawn from it to a fixed u a constant ratio to the dis- 



tance of the moving point from a given fixed point. 



27 '-a fixed point on a giv: ng along 



the circle, and Q the \*>\ ntection of the tangent at T with the 



perpendicular UJMUI it from /' ; find th- Incus of Q. 



. Use polar coordinates, P being the pole, and the diam- 



!ie initial 



28. r.-sd the length of the common chord of the two circlet 



(x-a)+(y-6) = r and (*- &)*+ (y -a) = H. 

 From this find the condition that these circles shall touch each other. 



29. If the axes are inclined at 60, prove that the equation 



represents a circle; find its radius and center. 



30. What is the obliquity of the axes if the equation 



represent* a circle? What is its radius? 



31. IT what point on the circle x + y* = 9 are the subtangent and 

 the subnormal of equal length? the tangent and normal? the tangent 

 snd sobUngent? 



