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(solved by Alexandre Nolin). Is there a triangle whose perimeter is less than 1 centimeter, while the radius of its circumscribed circle exceeds 1 kilometer?

This one wants a proof. Work it on paper, read the official solution, then mark yourself honestly — the ladder only means something if the record is true.

I solved it I didn't Skip

Official solution

. Yes. Take three points on the equator, less than 1 millimeter apart. They form a triangle for which the equator is the circumcircle.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.