1走义设P是否ABC所在平面内的一点，若a·PA＝b·PB＝c·PC．则称P是ABC的等积内．2等积点的性质性质1三角形的等积点在各边上射影所成三角形是等边三角形．证设P是ABC的等积点，作PH上BC、PE上CA、PF上AB，D、E、Fg重定，如图1．A、F、P、E四点并圆，目PA是直径，田正弦定理， 1 whether the escape function P is a point in the plane of ABC, if a·PA=b·PB=c·PC. Then P is called ABC’s equal product. 2 The properties of the isopleth point 1 The triangle’s equal product point is projected on each side. The triangle formed is an equilateral triangle. Assume that P is the isocratic point of ABC for PH on BC, PE on CA, PF on AB, D, E, Fg re-determined, as shown in Figure 1. A, F, P, E are four-point circle, and the target PA is the diameter, Tian Sine theorem,