The total power of a triangle is defined by P congruent 1/2(a_1^2 + a_2^2 + a_3^2), where a_i are the side lengths, and the "partial power" is defined by p_1 congruent 1/2(a_2^2 + a_3^2 - a_1^2).

altitude | circle power | perpendicular foot | triangle