Problem: A(2, 0), B(0, 2) and C are the vertices of a triangle inscribed in the circle $\large x^2 + y^2 = 4 $ . The bisector of angle C belongs to either of two families of concurrent lines, whose points of concurrency are
(A) (√2 , √2 )
(B) (-√2 , -√2 )
(C) (√2 , -√2 )
(D) (-√2 , √2 )
Ans: (A), (B).
Sol: The points of concurrency lie on the intersection of perpendicular bisectors of AB with the circle x2 + y2 = 4.
Hence the points are (√2 , √2 ) or (-√2 , -√2 )