Question

Three distinct points A, B and C are given in the two-dimensional coordinate plane such that the ratio of the distance of any one of them from the point (1, 0) to the distance from the point (−1, 0) is equal to 1/3.Then the circumcentre of the triangle ABC is at the point.

(A)  (0, 0)

(B)  (5/4,0)

(C) (5/2,0)

(D) (5/3,0)

Answer 1

Correct option  (B)  (5/4,0)

Let P = (1,0),Q(-1,0) and A = (x, y). Then

Therefore, A lies on the circle and similarly, B and C also lie on the same circle. Therefore, the circumcentre of ABC is the centre of the  circle 1, which is given by