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Length of Tangent and Power of a Point

Consider the ...

Question

Consider the circles $C_{1} \equiv x^{2} + y^{2} - 4 = 0$ , $C_{2} \equiv x^{2} + y^{2} - 6 x + 8 = 0$ , $C_{3} \equiv x^{2} + y^{2} - 8 x - 2 y + 16 = 0$ . The number of common tangents that can be drawn to touch at least two of the circle is

A

8

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B

9

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C

10

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D

12

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Solution

The correct option is A 8
Since for two circle the number of common tangents is $2^{2} = 4$

similarly the number of common tangents= $2^{3}$ =8.

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