In a triangle, `a^(2) + b^(2) + c^(2) = ca + ab sqrt(3)`. Then the triangles is :

Options

A. equilateral
B. right angled and isosceles
C. right angled and not isosceles
D. none of these

Explanation

we have,
`rArra^(2)+b^(2)+c^(2)=ac+sqrt3ab`
`rArr(a^(2))/4+c^(2)-ac+(3a^(2))/4+b^(2)-sqrt3ab=0`
`rArr(a/2-c)6(2)+((sqrt3a)/2-b)^(2)=0`
`rArra/2-c=0` and `(sqrt3)/2a-b=0`
`rArra=2c` and `sqrt3a=2b`
`rArra=(2b)/(sqrt3)=2c=lamda`(say)
`rArra=lamda,b=(sqrt3)/2lamda` and `c=(lamda)/2rArrb^(2)+c^(2)=a^(2)`
Hence, the triangle is right angled but not isosceles.