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MathLinks Contest 5th
4.1
4.1
Part of
MathLinks Contest 5th
Problems
(1)
0541 geometry 5th edition Round 4 p1
Source:
5/6/2021
Let
A
B
C
ABC
A
BC
be an acute angled triangle. Let
M
M
M
be the midpoint of
B
C
BC
BC
, and let
B
E
BE
BE
and
C
F
CF
CF
be the altitudes of the triangle. Let
D
≠
M
D \ne M
D
=
M
be a point on the circumcircle of the triangle
E
F
M
EFM
EFM
such that
D
E
=
D
F
DE = DF
D
E
=
D
F
. Prove that
A
D
⊥
B
C
AD \perp BC
A
D
⊥
BC
.
geometry
5th edition