Second Power Point

Given ∆ABC with sidelengths a = BC, b = CA and c = AB.
Let point Pa divides the segment BC in ratio BPa : PaC = c3 : b3. Let point Pb divides the segment CA in ratio CPb : PbA = a3 : c3, and let point Pc divides the segment AB in ratio APc : PcB = b3 : a3. Then the lines APa, BPb and CPc concur in a point known as the Second Power Point.



Point P = Second Power Point.