Let the points A : 0 , a , B : - 2,0 and C : 1 ,1 form an obtuse angled triangle (obtuse angled at angle A ), then the complete set of values of a is

Step-by-step solution

0 , a is a point that lies inside a circle whose end points of diameter are - 2,0 and 1,1 , but does not lie on this diameter. ⇒ 0 , a lies inside circle x + 2 x - 1 + y y - 1 = 0 ⇒ 0 + 2 0 - 1 + a a - 1 < 0 ⇒ a 2 - a - 2 < 0 ⇒ a - 2 a + 1 < 0 ⇒ a ∈ - 1,2 But a ≠ 2 3 because at a = 2 3 points 0 , 2 3 , - 2,0 & 1,1 are collinear ⇒ a ∈ - 1,2 - 2 3