Search any question & find its solution
Question:
Answered & Verified by Expert
In a triangle, if the ex-radii $r_1, r_2, r_3$ are in the ratio $1: 2: 3$, then its sides are in the ratio
Options:
Solution:
2785 Upvotes
Verified Answer
The correct answer is:
$5: 8: 9$
Given that, $r_1, r_2, r_3$ are ex-radii of triangle and
$$
\begin{aligned}
& r_1: r_2: r_3=1: 2: 3 \\
& r_1=x, r_2=2 x, r_3=3 x
\end{aligned}
$$
On adding Eqs. (i), (ii) and (iii), we get
$$
\begin{gathered}
3 s-(a+b+c)=\frac{\Delta}{x}+\frac{\Delta}{2 x}+\frac{\Delta}{3 x} \\
s=\frac{11 \Delta}{6 x}
\end{gathered}
$$
From Eqs. (i), (ii), (iii), we get
$$
a=\frac{5 \Delta}{6 x}, b=\frac{8 \Delta}{6 x}, c=\frac{9 \Delta}{6 x}
$$
So, $\quad a: b: c=5: 8: 9$.
$$
\begin{aligned}
& r_1: r_2: r_3=1: 2: 3 \\
& r_1=x, r_2=2 x, r_3=3 x
\end{aligned}
$$
On adding Eqs. (i), (ii) and (iii), we get
$$
\begin{gathered}
3 s-(a+b+c)=\frac{\Delta}{x}+\frac{\Delta}{2 x}+\frac{\Delta}{3 x} \\
s=\frac{11 \Delta}{6 x}
\end{gathered}
$$
From Eqs. (i), (ii), (iii), we get
$$
a=\frac{5 \Delta}{6 x}, b=\frac{8 \Delta}{6 x}, c=\frac{9 \Delta}{6 x}
$$
So, $\quad a: b: c=5: 8: 9$.
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.