Triangles And Properties Of Triangle Question 32
Question: In a triangle , if $ r_1=2r_2=3r_3, $ then $ \frac{a}{b}+\frac{b}{c}+\frac{c}{a} $ is equal to
Options:
A) $ \frac{75}{60} $
B) $ \frac{155}{60} $
C) $ \frac{176}{60} $
D) $ \frac{191}{60} $
Show Answer
Answer:
Correct Answer: D
Solution:
[d] Given that, $ r_1=2r_2=3r_3 $
$ \therefore \frac{\Delta }{s-a}=\frac{2\Delta }{s-b}=\frac{3\Delta }{s-c}=\frac{\Delta }{k} $ Then, $ s-a=k,s-b=2k,s-c=3k $
$ \Rightarrow 3s-(a+b+c)=6k\Rightarrow s=6k $
$ \therefore \frac{a}{5}=\frac{b}{4}=\frac{c}{3}=k $ Now, $ \frac{a}{b}+\frac{b}{c}+\frac{c}{a}=\frac{5}{4}+\frac{4}{3}+\frac{3}{5} $ $ =\frac{75+80+36}{60}=\frac{191}{60} $
BETA
