MathLabs

Problem 5

Determine, with proof, whether one can find 19751975 points on the circumference of a circle with unit radius such that the distance between any two of them is a rational number.
Step 3 of 5: Rational angles give rational chords
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AB=2sin⁡∠ABAB=2\sin\angle AB
Detailed analysis

For points A,BA,B on the unit circle, write ∠AB\angle AB for the relevant half central angle. The chord formula is AB=2sin⁡∠ABAB=2\sin\angle AB, so a good angle gives a rational chord.