The sides of ` A B C` satisfy the equation `2a^2+4b^2+c^2=4a b+2ac` Then a) the triangle is isosceles b) the triangle is obtuse c) `B=cos^(-1)(7/8)` d) `A=cos^(-1)(1/4)`

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)`