Let a triangle A B C be inscribed in the circle x 2 - 2 x + y + y 2 = 0 such that ∠ B A C = π 2 . If the length of side A B is 2 , then the area of the △ A B C is equal to:

Step-by-step solution

Given, circle x 2 - 2 x + y + y 2 = 0 With centre 1 2 , 1 2 and radius 1 . Since ∠ B A C = π 2 , so B C will act as diameter, B C = diameter = 2   (given) So, A C = B C 2 - A B 2 = 2 and A B = 2 Now, △ A B C = 1 2 A B · A C = 1