The Secant theorem relates two secants of a circle by the the point of intersection of the chords. It is used to define[br] [i]the power of a circle at a point.[/i]

PA * PB = PC * PD is true for any location of P. [br] However,[br][br]If P is outside,[br] |PB - PA| = AB (secant 1)[br] |PD - PC| = CD (secant 2)[br][br]P inside: [br] PB + PA = AB[br] PD + PC = CD[br][br]P on the circle:[br] PA*PD = PC*PD = 0[br] (One segment in each multiplication will always be zero.)[br] [br]If I want to assign meaning to this relationship, I should take the difference of sign into account. [br]For example, the power of a point is negative if P is inside the circle.[br][br]Onward.