Let P be an external point of a circle. Given two distinct secants PAB and PCD...

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Advance Math

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 âˆ’ ?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.

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GIVENP is an external point if a circle PAB and PCD are two distinctsecants of the circle such that B and CD are chords of the circleie PAB lie on a straight line where A and B lie on thecircumference of the circle and similarly PCD lie on a straightline See Answer

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