In a triangle ABC if `2Delta^(2)=(a^(2)b^(2)c^(2))/(a^(2)+b^(2)+c^(2))`, then it is

Options

A. equilateral
B. isosceles but not right angled
C. isosceles right angled
D. right angled

Answer

D

Explanation

We have
`2 Delta^(2)(a^(2)+b^(2)+c^(2))=a^(2)b^(2)c^(2)`
`therefore a^(2)+b^(2)+c^(2)=((abc)/(Delta))^(2).(1)/(2)=8R^(2)`
`therefore sin^(2)A+sin^(2)B+sin^(2)C=2`
`therefore cos 2A+cos 2B+cos 2C=-1`
`therefore -1-4 cos A cos B cos C=-1`
`therefore cos A cos B cos C = 0`
`cos a =0` or `cos B=0` or `cos C = 0`
`therefore` Triangle is right angled.