Mathematics

Problem

Three distinct points

A

B

and

C

are given in the 2-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)

\left(\frac{5}{4}, 0\right)

(b)

\left(\frac{5}{2}, 0\right)

(c)

\left(\frac{5}{3}, 0\right)

(d)

(0, 0)