Question

Polar of a point can exist only when the point is outside the circle.

• A. True
• B. False

Answer 1

The correct option is A

True

Lets see some special points in a circle. The concept of inverse points is one of them.In figure if

theres a point P on the plane of the circle then the inverse of the point P,say Q, is there such that

$OP.OQ=r^2$ where O,P,Q are colliner.So P and Q be inverse points with respect to a given circle.

$\overline{OP}.\overline{OQ}=r\times r$

Now we draw through Q a line p perpendicular to line PQ.(In the figure line p is the line joining the points

(T1,Q,T2). Then p is called the polar of the point p.The point p is called the pole of the line p,This polar

line passes through both T1 and T2 ,ie, the points where the tangents from p touches the cicle as shown

in the figure below.This gives a method for constructing the pole of an external point to the circle.

The polar can exists both when the points is inside and outside the circle. In limiting case of point lying on

the circle.the polar becomes the tangent of the circle at that point.

case 1

The polar can exists both when the point is inside and outside the circle. In limiting case of point lying on

the circle, the polar becomes the tangent of the circle at that point.

case 1

When point is inside any chord drawn meets circle at 2 point say A and B. The tangents are drawn from

A and B to intersect at T. Locus of all such $T_s$ is the polar.

case 2

For easier getting this point draw two tangents from p to the circle and connect the point of contacts. All

the above points will automatically fall on the same line.