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In a triangle ABC if 2Delta^(2)=(a^(2)b^...

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

A

equilateral

B

isosceles but not right angled

C

isosceles right angled

D

right angled

Text Solution

Verified by Experts

The correct Answer is:
D
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.
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