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Question

If the chord of contact of the circle $$x^{2}+y^{2}-2x+4y+\lambda=0$$ with respect to a point lying on the circle $$x^{2}+y^{2}-2x+4y+1=0$$ touches the circle $$x^{2}+y^{2}-2x+4y+3=0$$, then the number of value(s) of $$\lambda$$ is    


A
Zero
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B
One
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C
Two
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D
Infinitely many
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Solution

The correct option is A Zero
$$\rightarrow $$ AS both the circle have 
centers at $$ (1,-2)\left \{ (-g,-f) \right \} $$
$$ \Rightarrow $$ they are concentric circle 
$$ \Rightarrow $$  they can't have a chord 
of contact touching the
third circle which is also 
concentric to the two 
$$ \Rightarrow (A) $$

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