Metrical relations between the important lines in a triangle

In this note some original and very interesting metrical relations irvnlving certain important lines in a triangle are given.For exempla (Theorcm 2), if ABC is a nonisosceles trlangie and 11.,s,e denote the median, the sinedian drawing by A, and the angle between n, and renpocLively, then we have
m• or coca-L, ein (/),, a.) c:riNA- cosA cr.-v, c,:neli ain <(1)..m.)
(Lhe simedian is the symetriL of the blew:iris with respect to the median).