The sides of `DeltaABC` satisfy the equation `2a^(2) + 4b^(2) + c^(2) = 4ab + 2ac`. Then

Options

A. the triangle is isosceles
B. the triangle is obtuse
C. `B = cos^(-1) (7//8)`
D. `A = cos^(-1) (1//4)`

Answer

A, C, D

Explanation

`(a^(2) - 2ac + c^(2)) + (a^(2) - 4ab+ 4b^(2)) = 0`
or `(a-c)^(2) + (a-2b)^(2) = 0`
`rArr a = c and a = 2b`
Therefore, the triangle is isosceles.
Also, `cos B = (a^(2) + c^(2) -b^(2))/(2ac) = (7b^(2))/(8b^(2)) = (7)/(8)`
`cosA = (b^(2) + c^(2) -a^(2))/(2bc) = (1)/(4)`