Two tangents are drawn from the point P - 1 , 1 to the circle x 2 + y 2 - 2 x - 6 y + 6 = 0 . If these tangents touch the circle at points A and B , and if D is a point on the circle such that length of the segments A B and A D are equal, then the area of the triangle A B D is equal to:

Step-by-step solution

Given, the equation of circle is x 2 + y 2 - 2 x - 6 y + 6 = 0 So, the centre of the circle is 1 , 3 and the radius is 1 2 + 3 2 - 6 = 2 Assume, the coordinate of point B is - 1 , k and the coordinate of point A is h , 1 . So, h + 1 2 = 2 ⇒ h = 1 and k - 1 2 = 2 ⇒ k = 3 So, the coordinate of B is - 1 , 3 and the coordinate of A is 1 , 1 . From the diagram, area of ∆ A B D = 1 2 × 2 × 4 = 4 sq. units