WBJEE · Maths · Straight Lines
Two tangents to the circle \(x^{2}+y^{2}=4\) at the points \(A\) and \(B\) meet at \(M(-4,0)\). The area of the quadrilateral MAOB, where \(O\) is the origin is
- A \(4 \sqrt{3}\) sq. units
- B \(2 \sqrt{3}\) sq. units
- C \(\sqrt{3}\) sq. units
- D \(3 \sqrt{3}\) sq. units
Answer & Solution
Correct Answer
(A) \(4 \sqrt{3}\) sq. units
Step-by-step Solution
Detailed explanation
\begin{aligned} & O M=4, O A=2 \\ \therefore & M A=\sqrt{16-4}=\sqrt{12}=2 \sqrt{3} \\ \therefore & \text { Area }(M A O B) \\=& 2 \times \text { area } \Delta M A O \\=& 2 \times \frac{1}{2} \times M A \times O A \\=& 2 \sqrt{3} \times 2=4 \sqrt{3} \text { sq. units }…
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