Let tangents at two points A and B on circle x ^{2}+ y ^{2}-4 x +3=0 meet at origin O (0,0) . Then a

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10-1.Circle and System of Circles

hard

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

$\frac{3 \sqrt{3}}{2}$

C

$\frac{3}{2 \sqrt{3}}$

D

$\frac{3}{4 \sqrt{3}}$

(JEE MAIN-2022)

Solution

$C:(x-2)^{2}+y^{2}=1$

Equation of chord $AB : 2 x =3$

$OA = OB =\sqrt{3}$

$AM =\frac{\sqrt{3}}{2}$

$\text { Area of triangle } OAB =\frac{1}{2}(2 AM )( OM )$

$=\frac{3 \sqrt{3}}{4} sq . \text { units }$

Standard 11

Mathematics

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