Question

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 1

Answer: (B)

Equation of chord $AB : 2 x =3$

$ OA = OB =\sqrt{3} $
$ AM =\frac{\sqrt{3}}{2}$
Area of triangle $OAB =\frac{1}{2}(2 AM )( OM )$
$=\frac{3 \sqrt{3}}{4}$ sq. units