A) \[2:3:5\]
B) \[1:2:3\]
C) \[1:3:7\]
D) \[3:7:9\]
Correct Answer: B
Solution :
We have;\[\Delta =\frac{\sqrt{3}}{4}{{a}^{2}},\,\,s=\frac{abc}{4\Delta }\] \[\therefore \] \[r=\frac{\Delta }{S}=\frac{a}{2\sqrt{3}},\,\,R=\frac{abc}{4\Delta }\] \[=\frac{{{a}^{3}}}{\sqrt{3}\cdot {{a}^{2}}}=\frac{a}{\sqrt{3}}\] and \[{{r}_{1}}=\frac{\Delta }{S-a}=\frac{\sqrt{3}/4\cdot {{a}^{2}}}{a/2}=\frac{\sqrt{3}}{2}\] Hence; \[r:R:{{r}_{1}}=\frac{a}{2\sqrt{3}}:\frac{a}{\sqrt{3}}:\frac{\sqrt{3}}{2}\cdot a=1:2:3\]
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