Question

In $\triangle A B C$ if $( a + b + c ) ( a - b + c )$=3ac, then.

• A. $\angle B = 60 ^ { \circ }$
• B. $\angle B = 30 ^ { \circ }$
• C. $\angle C = 60 ^ { \circ }$
• D. $\angle A + \angle C = 90 ^ { \circ }$

Answer 1

Answer: (A)

$\angle B = 60 ^ { \circ }$

Answer 2

$( a + c ) ^ { 2 } - b ^ { 2 } = 3 a c \Rightarrow a ^ { 2 } + c ^ { 2 } - b ^ { 2 } = a c$

But $\cos B = \frac { a ^ { 2 } + c ^ { 2 } - b ^ { 2 } } { 2 a c } = \frac { 1 } { 2 } \Rightarrow B = \frac { \pi } { 3 }$.