Class 11

29.Circle and System of Circles question bank (Maths)

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Q1.

Two circles with radii \( r_1 \) and \( r_2 \) (\( r_2 > r_1 \ge 2 \)) touch each other externally.  
If \( \theta \) be the angle between the direct common tangents, then  

(A)
\( \theta = \sin^{-1}\left(\frac{r_1 + r_2}{r_1 - r_2}\right) \)
(B)
\( \theta = 2\sin^{-1}\left(\frac{r_2 - r_1}{r_1 + r_2}\right) \)
(C)
\( \theta = \sin^{-1}\left(\frac{r_1 - r_2}{r_1 + r_2}\right) \)
(D)
none of these
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Q2.

The chords of contact of the pair of tangents drawn from each point on the line \(2x + y = 4\) to the circle \(x^2 + y^2 = 1\) pass through a fixed point.  

(A)
(2, 4)
(B)
\((- \frac{1}{2}, -\frac{1}{4})\)
(C)
\((\frac{1}{2}, \frac{1}{4})\)
(D)
(-2, -4)
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