A) right angled
B) isosceles
C) equilateral
D) None of these
Correct Answer: A
Solution :
Given, \[\left( 1-\frac{{{r}_{1}}}{{{r}_{2}}} \right)\left( 1-\frac{{{r}_{1}}}{{{r}_{2}}} \right)=2\] \[\therefore \] \[\left( 1-\frac{s-b}{s-a} \right)\left( 1-\frac{s-c}{s-a} \right)=2\] \[\Rightarrow \] \[\frac{(b-a)(c-a)}{{{(s-a)}^{2}}}=2\] \[\Rightarrow \] \[{{a}^{2}}={{b}^{2}}+{{c}^{2}}\] Hence, triangle is a right angled triangle.
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