Question

The maximum number of points with rational coordinates on a circle with radius $2$ & whose centre is $(\sqrt{3},0)$ is

• A. one
• B. two
• C. four
• D. infinite

Answer 1

Answer: (B)

two

Equation of circle $(x-\sqrt{3}{)}^2+(y-0{)}^2=4(x-\sqrt{3}{)}^2+y^2=4$

For being circumcentre of a triangle having rational coordinates, the circumcentre should also have a rational coordinate.

Since $(\sqrt{3},0)$ cannot be the circumcentre of a triangle in a circle. Maximum rational point are $2$