Home
Class 12
MATHS
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.
Promotional Banner

Topper's Solved these Questions

  • SOLUTIONS AND PROPERTIES OF TRIANGLE

    CENGAGE|Exercise Multiple Correct Answers Type|13 Videos

  • SOLUTIONS AND PROPERTIES OF TRIANGLE

    CENGAGE|Exercise Comprehension Type|6 Videos

  • SETS AND RELATIONS

    CENGAGE|Exercise Question Bank|15 Videos

  • STATISTICS

    CENGAGE|Exercise JEE Previous Year|10 Videos

Similar Questions

Explore conceptually related problems

In a triangle ABC. If triangle^(2) = (a^(2)b^(2)c^(2))/(2(a^(2)+b^(2)+c^(2)) , where triangle is the area of the triangle, then the triangle is

In triangle, ABC if 2a^(2) b^(2) + 2b^(2) c^(2) = a^(4) + b^(4) + c^(4) , then angle B is equal to

In triangle ABC(a^(2)-b^(2)-c^(2))tan A+(a^(2)-b^(2)+c^(2))tan B=

In triangle ABC,/_C=90^(@) then (a^(2)-b^(2))/(a^(2)+b^(2))=

In a triangle ABC, if (a+b+c)(a+b-c)(b+c-a)(c+a-b)=(8a^(2)b^(2)c^(2))/(a^(2)+b^(2)+c^(2)) then the triangle is

In a triangle ABC, if (a+b+c)(a-b)^(2)+(b-c)^(2)+(c-a)^(2))=2c^(2)(a+b+c)-6abc, then

In triangle ABC,C=90^(@). Then (a^(2)-b^(2))/(a^(2)+b^(2))=

In a triangle ABC,cos^(2)A+cos^(2)B+cos^(2)C=

In a triangle ABC,a^(2)cos^(2)A=b^(2)+c^(2) then triangle is

If a, b, c are the sides of Delta ABC such that 3^(2a^(2))-2*3^(a^(2)+b^(2)+c^(2))+3^(2b^(2)+2c^(2))=0 , then Triangle ABC is