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the line joining the point of intersection, K, of SD and S’’D” with S’, the vertex 
of T’S’ is a Simson’s line conjugate to T’S’. 
Let ES and FS” intersect at K, and ES” and FS intersect at N (Fig. 3). 
Since the pair of lines, ES, FS and ES”, FS” are conjugate Simson’s lines, they 
4 
are | to each other, or ES” and FS are altitudes in the (\ EKF. Therefore KN 
is the third altitude, and we may prove S to be the foot of this altitude on EF. 
The nine-point circle of the /\ ABC passing through the feet, S and 8S”, of the 
two altitudes, and through the middle point, T’, of one side of the (\ EKF, must 
