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

Step-by-step solution

Given 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 , Plotting the diagram we get, Now circle C : x - 2 2 + y 2 = 1 Equation of chord A B is given by T = 0 i.e x × 0 + y × 0 - 4 x + 0 2 + 3 = 0 ⇒ A B : 2 x = 3 Now O A = O B = 0 2 + 0 2 - 4 × 0 + 3 = 3 So, AM = O A 2 - O M 2 = 3 - 9 4 = 3 4 = 3 2 Now area of triangle O A B = 1 2 2 A M O M = 3 3 4 sq. units