Question

Let the tangents at two points A and B on the circle$x^2 + y^2 – 4x + 3 = 0$ meet at origin O(0, 0). Then the area of the triangle OAB is

• A. $\frac{3\sqrt3}{2}$
• B. $\frac{3\sqrt3}{4}$
• C. $\frac{3}{2\sqrt3}$
• D. $\frac{3}{4\sqrt3}$

Answer 1

Answer: (B)

$\frac{3\sqrt3}{4}$

Answer 2

$C:(x-2)² + y² = 1$

Equation of chord AB: 2x = 3

OA = OB = $\sqrt3$

AM = $\frac{\sqrt3}{{2}}$

Area of triangle OAB

$=\frac{1}{2}(2AM) (OM)$

=$\frac{3\sqrt3}{4}$sq. units