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Intersection between Tangent and Secant

If a line is ...

Question

If a line is drawn through a point $A (3, 4)$ to cut the circle $x^{2} + y^{2} = 4$ at $P$ and $Q$ then $A P . A Q =$

A

15

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B

17

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C

21

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D

25

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Solution

The correct option is C $21$
Given point $A (3, 4)$ and circle $x^{2} + y^{2} = 4$
For a circle $A P A R = A T^{2}$
$A T^{2} = 3^{2} + 4^{2} - 4$
$= 25 - 4 = 21$ units.

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