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TOT 275 1990 Autumn O S3 two identical clocks on wall

Source:

June 8, 2024
geometryalgebrageometric inequality

Problem Statement

There are two identical clocks on the wall, one showing the current Moscow time and the other showing current local time. The minimum distance between the ends of their hour hands equals mm and the maximum distance equals MM. Find the distance between the centres of the clocks.
(S Fomin, Leningrad)