Question

a
Q55. In
triangle ABC if
(a + b + c)(b + c-a) = 3 bc then
(A) A = 60°
(B) B = 60°
(C) C = 60°
(D) A = 90°
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Answer 1

Answer:

ANSWER

(b+c+a)(b+c−a)=(b+c)

2

−a

2

=b

2

+c

2

+2bc−a

2

......(1)

Substituting (1) in the given expression, we get

b

2

+c

2

−a

2

=3bc−2bc

That gives,

2bc

b

2

+c

2

−a

2

=

2

1

......(2)

We also know, by cosine law that cosA=

2bc

b

2

+c

2

−a

2

.

By equation (2), cosA=

2

1

or A=60

∘

. Option A is correct.