In a Δ A B C ,   2 Δ 2 = a 2 b 2 c 2 a 2 + b 2 + c 2 , then the triangle is

We have, $2{\Delta }^2(a^2+b^2+c^2)=a^2{b}^2{c}^{2 }$

$\Rightarrow (a^2+b^2+c^2)={\left(\frac{abc}{\Delta }\right)}^2.\frac{1}{2}=8R^2$

$\Rightarrow {\sin }^{2}A+{\sin }^{2}B+{\sin }^{2}C=2$

$\Rightarrow {\cos }^{2}A+{\cos }^{2}B+{\cos }^{2}C=-1$

$\Rightarrow -1- 4\cos A\cos B\cos C=-1$

$\therefore \cos A\cos B\cos C=0$

$\Rightarrow \cos a=0 \text{or} \cos B=0 \text{or} \cos C=0$

Therefore, any one of the angle is $90°$, hence, it is a right angled triangle