Question

If in a $\Delta ABC$; $b^{2}sin2C+c^{2}sin2B=2bc$, then the triangle is

• A. equilateral
• B. isosceles with $\angle B=\angle C$
• C. right angled at A
• D. none of these

Answer 1

The correct option is C right angled at A

$b^{2}sin2C+c^{2}sin2B=2bc$
$\Rightarrow 4R(b\sin B\sin C\cos C+c\sin C\sin B\cos B)=2\left(2R\sin B\right)\left(2R\sin C\right)$ [ from sine rule]
$\Rightarrow b\cos C+c\cos B=2R$
$\Rightarrow a=2R$ [ from projection rule ]
Therefore, from sine rule $A=\frac{\pi }{2}$
Ans: C