(B) For a point $P(x_1, y_1)$ outside a circle $S: x^2 + y^2 + 2gx + 2fy + c = 0$,the power of the point is given by $S_1 = x_1^2 + y_1^2 + 2gx_1 + 2f

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(B) For a point $P(x_1, y_1)$ outside a circle $S: x^2 + y^2 + 2gx + 2fy + c = 0$,the power of the point is given by $S_1 = x_1^2 + y_1^2 + 2gx_1 + 2fy_1 + c$.By the theorem of intersecting chords (or power of a point),for a line through $P$ intersecting the circle at $A$ and $B$,$PA \cdot PB = |S_1|$.Given $P(3, 11)$ and the circle $x^2 + y^2 - 9 = 0$,we have $S_1 = (3)^2 + (11)^2 - 9$.$S_1 = 9 + 121 - 9 = 121$.Therefore,$PA \cdot PB = 121$.

Class 11 Mathematics 10-1.Circle and System of Circles Geometrical problems regarding circle and its properties

Easy

$A$ line passing through the point $P(3, 11)$ intersects the circle $x^{2} + y^{2} = 9$ at points $A$ and $B$. Then $PA \cdot PB = . . . . .$

A
$9$
B
$121$
C
$205$
D
$139$

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10-1.Circle and System of Circles

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Geometrical problems regarding circle and its properties

The triangle $PQR$ is inscribed in the circle $x^2+y^2=25$. If $Q=(3,4)$ and $R=(-4,3)$,then $\angle QPR=$

EasyAP EAMCET 2024

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DifficultMHT CET 2019

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Lines are drawn from a point $P(-1, 3)$ to a circle $x^2 + y^2 - 2x + 4y - 8 = 0$. If the line meets the circle at two points $A$ and $B$,then the minimum value of $PA + PB$ is:

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If the line $y - 1 = m(x - 1)$ intersects the circle $x^2 + y^2 = 4$ at two distinct points,then the number of possible values of $m$ is:

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The circles $x^2 + y^2 - 10x + 16 = 0$ and $x^2 + y^2 = r^2$ intersect each other in two distinct points,if

DifficultIIT 1994

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$A$ line passing through the point $P(3, 11)$ intersects the circle $x^{2} + y^{2} = 9$ at points $A$ and $B$. Then $PA \cdot PB = . . . . .$

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The triangle $PQR$ is inscribed in the circle $x^2+y^2=25$. If $Q=(3,4)$ and $R=(-4,3)$,then $\angle QPR=$

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