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The sides of DeltaABC satisfy the equati...

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

A

the triangle is isosceles

B

the triangle is obtuse

C

`B = cos^(-1) (7//8)`

D

`A = cos^(-1) (1//4)`

Text Solution

Verified by Experts

The correct Answer is:
A, C, D
`(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)`
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