COMEDK · Maths · 19. Properties of Triangles
In a \(\triangle A B C\) if \(b=2, B=30^{\circ}\) then the area of the circumcircle of \(\triangle A B C\) in square units is
- A \(\pi\)
- B \(2 \pi\)
- C \(4 \pi\)
- D \(6 \pi\)
Answer & Solution
Correct Answer
(C) \(4 \pi\)
Step-by-step Solution
Detailed explanation
We have, \[ \frac{b}{\sin B}=2 R \] \(\Rightarrow \quad R=\frac{B}{2 \sin B}=\frac{2}{2 \times \sin 30^{\circ}}=2\) \(\therefore\) Area of circumcircle \(=\pi R^{2}\) \(=\pi(2)^{2}=4 \pi\)
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