The total Power of a Triangle is defined by

(1) 
where are the side lengths, and the ``partial power'' is defined by

(2) 
Then

(3) 

(4) 

(5) 

(6) 

(7) 

(8) 

(9) 
where is the Area of the Triangle and are the Feet of the Altitudes. Finally, if a side of the Triangle and the value of any partial power are given, then the Locus of
the third Vertex is a Circle or straight line.
See also Altitude, Foot, Triangle
References
Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA:
Houghton Mifflin, pp. 260261, 1929.
© 19969 Eric W. Weisstein
19990526