107 
fee. and bb osare concyclic and. 4 PPO 72 PP) C= 902 and 
Bee LAC: 
.*. P, Dis Simson’s line of P. 
The point where PH cuts Simson’s line of P is called its center. 
11. The line joining A’, the point opposite the vertex A of /\ ABC (Fig. 4), 
with H, the ortho-centre, bisects the side BC. 
For, the Simson line of A’ is BC, .*. BC bisects A’ H, and, as we have 
shown, this bisection is on the nine-point circle. But the nine-point circle cuts 
BC at two places only, at Ha and Ma; hence it is obvious that A’ H passes through 
Ma, and thus it bisects BC. 
12. S, the intersection of the Simson lines of P and Q, the extremities of any 
diameter of the circumcircle, lies on the nine-point circle. (Fig. 3.) 
