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Polyline inscribed in an arc

Source: Kvant Magazine No. 1 2020, 50th Anniversary, M1000

March 10, 2023

geometrycirclesKvant

Problem Statement

A polyline

AMB

is inscribed in the arc

AB{}

, consisting of two segments, and

AM>MB

. Let

K

be the midpoint of the arc

AB{}

. Prove that the foot

H{}

of the perpendicular from

K

onto

AM

divides the polyline in two equal segments:

AH=HM+MB.

Discovered by Archimedes

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