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  • Two circles with radii <img alt="\mathrm{\text { ' } r_1 \text { ' and ' } r_2 \text { ', } r_1>r_2 \geq 2}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%5Ctext%20%7B%2

Two circles with radii \mathrm{\text { ' } r_1 \text { ' and ' } r_2 \text { ', } r_1>r_2 \geq 2} , touch each other externally. If \mathrm{\Theta }  be the angle between

the direct common tangents, then

Option: 1

\mathrm{\theta=\sin ^{-1}\left(\frac{r_1+r_2}{r_1-r_2}\right)}


Option: 2

\mathrm{\theta=2 \sin ^{-1}\left(\frac{r_1-r_2}{r_1+r_2}\right)}


Option: 3

\mathrm{\theta=\sin ^{-1}\left(\frac{r_1-r_2}{r_1+r_2}\right)}


Option: 4

none of these


Answers (1)

best_answer

 \mathrm{\begin{aligned} & \sin \alpha=\frac{r_1-r_2}{r_1+r_2} \\\\ & \Rightarrow \theta=2 \sin ^{-1}\left(\frac{r_1-r_2}{r_1+r_2}\right) \end{aligned}}                                                                   

Hence (b) is correct

Posted by

sudhir.kumar

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