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a circle with center (0,root 2) then at most two rational points may be on the circle ??............. how ??

a circle with center (0,root 2) then at most two rational points may be on the circle ??............. how ??

Grade:

1 Answers

SAGAR SINGH - IIT DELHI
879 Points
10 years ago

Dear atul,

for k=2

Let A and B be two points on the circumference of a circle radius r. The chord AB subtending an angle x at the centre. For 0<= x <= pi let f:x-->length AB

f is a continuous function 0<= f(x) <=2r

there exists a positive integer n such that 2^(-n) <2r and so there is a chord of rational length.

Thus there are 2 rational points on the circle.

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Sagar Singh

B.Tech, IIT Delhi

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