The Secant Theorem
- Ryan Hirst
The Secant theorem relates two secants of a circle by the the point of intersection of the chords. It is used to define the power of a circle at a point.
PA * PB = PC * PD is true for any location of P. However, If P is outside, |PB - PA| = AB (secant 1) |PD - PC| = CD (secant 2) P inside: PB + PA = AB PD + PC = CD P on the circle: PA*PD = PC*PD = 0 (One segment in each multiplication will always be zero.) If I want to assign meaning to this relationship, I should take the difference of sign into account. For example, the power of a point is negative if P is inside the circle. Onward.