Question

$\mathrm{In}\Delta \mathrm{ABC},\mathrm{if}(a+b+c)(a-b+c)=3\mathrm{ac},\mathrm{then}\angle B=$ .

• A. $\frac{\pi }{4}$
• B. $\frac{\pi }{6}$
• C. $\frac{\pi }{2}$
• D. $\frac{\pi }{3}$

Answer 1

The correct option is D $\frac{\pi }{3}$

$(a+b+c)(a-b+c)=3\mathrm{ac}\Rightarrow {(a+c)}^2-b^2=3\mathrm{ac}\mathrm{or}{a}^2+c^2-b^2=\mathrm{ac}\mathrm{Also},\cos B=\frac{a^2+c^2-b^2}{2\mathrm{ac}}=\frac{1}{2}\Rightarrow \angle B=\frac{\pi }{3}$