Question : When two circles of radii $r_1$ and $r_2$ have their centres at a distance $d$ apart, the length of the common transverse tangent is:
Option 1: $\sqrt{d^2-\left(r_1-r_2\right)^2}$
Option 2: $\sqrt{d^2+\left(r_1-r_2\right)^2}$
Option 3: $\sqrt{d-\left(r_1-r_2\right)^2}$
Option 4: $\sqrt{d^2-\left(r_1+r_2\right)^2}$
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Correct Answer: $\sqrt{d^2-\left(r_1+r_2\right)^2}$
Solution :
The distance between the centres of the two circles is $d$.
If the radii are r
1
and r
2
, the length of their transverse common tangent is $\sqrt{d^{2}-(r_{1} + r_{2})^{2}}$.
Hence, the correct answer is $\sqrt{d^{2}-(r_{1} + r_{2})^{2}}$.
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