A) \[\frac{16}{9}\]
B) \[\frac{16}{7}\]
C) \[\frac{11}{7}\]
D) \[\frac{7}{16}\]
Correct Answer: B
Solution :
We have \[R=\frac{abc}{4\Delta }\] and \[r=\frac{\Delta }{s}\] \[\Rightarrow \] \[\frac{R}{r}=\frac{abc}{4\Delta }.\frac{s}{\Delta }=\frac{abc}{4\,(s-a)\,(s-b)(s-c)}\] Since \[a:b:c=4:5:6;\,\frac{a}{4}=\frac{b}{5}=\frac{c}{6}=k\,(\text{say})\] Thus \[\frac{R}{r}=\frac{(4k)\,(5k)\,(6k)\,}{4\,\left( \frac{15k}{2}-4k \right)\,\left( \frac{15k}{2}-5k \right)\,\left( \frac{15k}{2}-6k \right)}=\frac{16}{7}\].
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