Question

If in a $△ABC,r_1=2r_2=3r_3,$ then:

• A. $\frac{a}{b}=\frac{4}{5}$
• B. $\frac{a}{b}=\frac{5}{4}$
• C. $\frac{a}{c}=\frac{3}{5}$
• D. $\frac{a}{c}=\frac{5}{3}$

Answer 1

Answer: (B), (D)

The correct options are
B $\frac{a}{b}=\frac{5}{4}$
D $\frac{a}{c}=\frac{5}{3}$

Since $r_1=2r_2=3r_3=k$(say)
$\frac{△}{s-a}=k;\frac{△}{s-b}=k;\frac{△}{s-c}=k$
$\therefore s-a=\frac{△}{k};s-b=\frac{2△}{k}$ and $s-c=\frac{3△}{k}$
Adding
$s-a+s-b+s-c=\frac{△}{k}+\frac{2△}{k}+\frac{3△}{k}=\frac{6△}{k}$
$\Rightarrow a=s-\frac{△}{k}=\frac{6△}{k}-\frac{△}{k}=\frac{5△}{k}$
$\Rightarrow b=s-\frac{2△}{k}=\frac{6△}{k}-\frac{2△}{k}=\frac{4△}{k}$
$\Rightarrow c=s-\frac{3△}{k}=\frac{6△}{k}-\frac{3△}{k}=\frac{3△}{k}$
$\therefore \frac{a}{b}=\frac{5}{4}$ and $\frac{a}{c}=\frac{5}{3}$