A) \[2:1\]
B) \[\sqrt{3}:1\]
C) \[\sqrt{5}:1\]
D) \[4:1\]
Correct Answer: B
Solution :
Here, let O,O' be the centres of the circle. |
As, the centre of each lies on the circumference of the other. The two circles will have the same radius. Let it be r. |
\[\therefore \] \[OC=O'C=\frac{r}{2}\] |
\[\therefore \] \[AC=\sqrt{O{{A}^{2}}-O{{C}^{2}}}=\sqrt{{{r}^{2}}-\frac{{{r}^{2}}}{4}}=\frac{\sqrt{3}}{2}r\] |
Hence, \[\frac{\text{Common}\,\,\text{chord}}{\text{Radius}}=\frac{\frac{\sqrt{3}r}{2}}{\frac{r}{2}}=\frac{\sqrt{3}}{1}=\sqrt{3}:1\] |
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