Manchester Memoirs, Vol. lix. (191 5), No. 13. 25 



V. Another method of trisecting an angle involving 

 the drawing of a tangent was suggested to one of the 

 authors by the fact that a limacon is a pedal curve to a 

 fixed circle with reference to a fixed point. Let ABC 

 {Fig. 18) be the angle to be trisected. With any point A 



Fig. 18. (New Method.) 



as centre and AB as radius describe a circle. Produce 

 AB, making BD equal to AB. Find a point P on AC 

 such that PD is perpendicular to a tangent drawn to the 

 circle through P. Then if E be the point of contact and 

 if PE be bisected at F, BE and />F are obviously the 

 trisectors of the angle ABC. 



The point P may readily be found by using a rect- 

 angular card or a set-square, and, keeping one of the 

 corners on the line BC, moving the card until one of the 

 adjacent sides touches the circle while the other passes 

 through /). 



