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Question

In ΔABC, if(a+b+c)(ab+c)=3ac,then B= .

A
π4
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B
π6
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C
π2
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D
π3
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Solution

The correct option is D π3
(a+b+c)(ab+c)=3ac(a+c)2b2=3acor a2+c2b2=acAlso, cos B=a2+c2b22ac=12B=π3

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