JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
Let the tangents at two points \(A\) and \(B\) on the circle \(x ^{2}+ y ^{2}-4 x +3=0\) meet at origin \(O (0,0)\). Then the area of the triangle of \(OAB\) is.
- A \(\frac{3 \sqrt{3}}{2}\)
- B \(\frac{3 \sqrt{3}}{4}\)
- C \(\frac{3}{2 \sqrt{3}}\)
- D \(\frac{3}{4 \sqrt{3}}\)
Answer & Solution
Correct Answer
(B) \(\frac{3 \sqrt{3}}{4}\)
Step-by-step Solution
Detailed explanation
\(C:(x-2)^{2}+y^{2}=1\) Equation of chord \(AB : 2 x =3\) \(OA = OB =\sqrt{3}\) \(AM =\frac{\sqrt{3}}{2}\) \(\text { Area of triangle } OAB =\frac{1}{2}(2 AM )( OM )\) \(=\frac{3 \sqrt{3}}{4} sq . \text { units }\)
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