Question

If in a triangle $\frac{r}{r_1}=\frac{r_2}{r_3},$ where $r,r_1,r_2,r_3$ have their usual meaning, then

• A. $A={90}^0$
• B. $B={90}^0$
• C. $C={90}^0$
• D. None of these

Answer 1

The correct option is C $C={90}^0$

Given $\frac{r}{r_1}=\frac{r_2}{r_3}$

$\Rightarrow \frac{\Delta (s-a)}{s\Delta }=\frac{\Delta (s-c)}{(s-b)\Delta }$

$\Rightarrow (s-a)(s-b)=s(s-c)$

$\Rightarrow ab=s(a+b+c)$

$\Rightarrow a^2+b^2=c^2$

$\Rightarrow$ the triangle is right angled at $C$.