A) \[{{r}_{1}}{{r}_{2}}\]
B) \[\sqrt{(r_{1}^{2}+r_{2}^{2}})\]
C) \[{{r}_{1}}{{r}_{2}}\sqrt{(r_{1}^{2}+r_{2}^{2})}\]
D) \[\frac{{{r}_{1}}{{r}_{2}}}{\sqrt{(r_{1}^{2}+r_{2}^{2})}}\]
Correct Answer: D
Solution :
In \[\Delta OPC\], \[\cos \theta =\frac{r}{{{r}_{1}}}\] In \[\Delta O'PC\], \[\sin \theta =\frac{r}{{{r}_{2}}}\] As, \[{{\cos }^{2}}\theta +{{\sin }^{2}}\theta =1\] \ \[{{\left( \frac{r}{{{r}_{1}}} \right)}^{2}}+{{\left( \frac{r}{{{r}_{2}}} \right)}^{2}}=1\]Þ \[r=\frac{{{r}_{1}}{{r}_{2}}}{\sqrt{r_{1}^{2}+r_{2}^{2}}}\].You need to login to perform this action.
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