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Position of a point with respect to circle

A line drawn ...

Question

A line drawn through the point $P (4, 7)$ cuts the circle $x^{2} + y^{2} = 9$ at the point A and B. Then PA. PB is equl to

53

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56

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74

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65

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Solution

The correct option is B $56$
Give circle $x^{2} + y^{2} = 9$
at point $P (4, 7)$
$P A = P B = P T^{2}$ (i.e., $(l e n g t h o f t a n g e n t s)^{2}$ ) from $(4, 7)$
$= x^{2} + y^{2} - 9$
$= (4)^{2} + (7)^{2} - 9$
$= 16 + 49 - 9$
$= 56$ .

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