Let P be an external point of a circle. Given two distinctsecants PAB and PCD such that AB
and CD are chords of the circle. We know that PA x PB = PC xPD.
(a) Alternatively, if the point P lies on the circle, i.e., P movesfrom being an external point
to become concurrent with A and C, state why PA x PB = PC x PD isstill obtained.
(b) It can be shown that PA x PB = PC x PD even if P is an internalpoint of a circle. The
power of a point P with respect to a circle is defined as ?2 − ?2where d is the distance
from P to the centre of the circle and R is the radius of thecircle. Using the results above,
determine the three possible locations of P when its power is zero,positive and negative,
respectively.
