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Kvant 2020
M1000
M1000
Part of
Kvant 2020
Problems
(1)
Polyline inscribed in an arc
Source: Kvant Magazine No. 1 2020, 50th Anniversary, M1000
3/10/2023
A polyline
A
M
B
AMB
A
MB
is inscribed in the arc
A
B
AB{}
A
B
, consisting of two segments, and
A
M
>
M
B
AM>MB
A
M
>
MB
. Let
K
K
K
be the midpoint of the arc
A
B
AB{}
A
B
. Prove that the foot
H
H{}
H
of the perpendicular from
K
K
K
onto
A
M
AM
A
M
divides the polyline in two equal segments:
A
H
=
H
M
+
M
B
.
AH=HM+MB.
A
H
=
H
M
+
MB
.
Discovered by Archimedes
geometry
circles
Kvant