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Question

In ABC, if (a+b+c)(a-b+c)=3ac, then


A

B=60°

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B

B=30°

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C

C=60°

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D

A+C=90°

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Solution

The correct option is A

B=60°


Explanation for the correct Option:

Determining the angle In ABC

(a+b+c)(a-b+c)=3ac[Given]((a+c)+b)((a+c)b)=3ac(a+c)2b2=3aca2+c2+2acb23ac=0a2+c2b2=ac(i)

We know the cosine rule in ABC, having sides a,b,c

cosB=(a2+c2b2)2ac

Putting (i) in cosB we get

cosB=ac2accosB=12cosB=cos60°B=60°

Hence, option A is the correct answer.


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