Let the tangents at two points A and B on the circle x2+y2-4 x+3=0 meet at origin O (0,0). Then the area of the triangle of OAB is

Question

Let the tangents at two points A and B on the circle x2+y2-4 x+3=0 meet at origin O (0,0). Then the area of the triangle of OAB is (A) (3 √3/2) (B) (3 √3/4) (C) (3/2 √3) (D) (3/4 √3)

Tardigrade Admin · Accepted Answer

Equation of chord AB: 2 x =3 <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/44b24d29af641f6ef218ade6158ba31a-.png" /> OA = OB =√3 AM =(√3/2) Area of triangle OAB =(1/2)(2 AM )( OM ) =(3 √3/4) sq. units

Q. 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 $O A B$ is

$\frac{3 3}{2}$

$\frac{3 3}{4}$

$\frac{3}{2 3}$

$\frac{3}{4 3}$

Equation of chord $A B : 2 x = 3$

$O A = OB = 3$
$A M = \frac{3}{2}$
Area of triangle $O A B = \frac{1}{2} (2 A M) (OM)$
$= \frac{3 3}{4}$ sq. units

Q. Let the tangents at two points A and B on the circle x2+y2−4x+3=0 meet at origin O(0,0). Then the area of the triangle of OAB is

233​​

433​​

23​3​

43​3​