Trigonometric Equations Question 68
Question: In a triangle ABC, $ a:b:c=4:5:6 $ . The ratio of the radius of the circumcircle to that of the incircle is
[IIT 1996]
Options:
A) $ \frac{16}{9} $
B) $ \frac{16}{7} $
C) $ \frac{11}{7} $
D) $ \frac{7}{16} $
Show Answer
Answer:
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,(say) $ Thus $ \frac{R}{r}=\frac{(4k),(5k),(6k),}{4,( \frac{15k}{2}-4k ),( \frac{15k}{2}-5k ),( \frac{15k}{2}-6k )}=\frac{16}{7} $ .
BETA
