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Chile Contests
The Golden Number Mathematics Tournament
TNO 2023
3
3
Part of
TNO 2023
Problems
(1)
American geo in chile :o
Source:
10/31/2024
Let
△
A
B
C
\triangle ABC
△
A
BC
be an acute triangle with orthocenter
H
H
H
, and let
M
M
M
be the midpoint of
B
C
BC
BC
. Let
P
P
P
be the foot of the perpendicular from
H
H
H
to
A
M
AM
A
M
. Prove that
A
M
⋅
M
P
=
B
M
2
AM \cdot MP = BM^2
A
M
⋅
MP
=
B
M
2
.
geometry
Chile