Madhya Pradesh Police Exam Model Paper 10

Given:
O is the circumcenter of the triangle ΔABC and ∠BOC = 40°
Concept Used:
If O is the circumcenter of ΔABC then the angle made at the circumcenter by joining any two vertices of the triangle is twice the angle at the third vertex of the triangle i.e. the angle made at the circumference at the circle.
Calculation:O is the circumcenter of ΔABC and ∠BOC = 40°
$\angle \mathit{B}\mathit{A}\mathit{C}=\left(1/2\right)\times \angle \mathit{B}\mathit{O}\mathit{C}$
$\Rightarrow \angle \mathit{B}\mathit{A}\mathit{C}=\left(1/2\right)\times 40°$
$\Rightarrow \angle \mathit{B}\mathit{A}\mathit{C}=20°$
∴ The value of ∠BAC is 20°