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Canadian Junior Mathematical Olympiad
2022 Canadian Junior Mathematical Olympiad
1
1
Part of
2022 Canadian Junior Mathematical Olympiad
Problems
(1)
Easy geometry
Source: CJMO 2022 P1
3/12/2022
Let
△
A
B
C
\triangle{ABC}
△
A
BC
has circumcircle
Γ
\Gamma
Γ
, drop the perpendicular line from
A
A
A
to
B
C
BC
BC
and meet
Γ
\Gamma
Γ
at point
D
D
D
, similarly, altitude from
B
B
B
to
A
C
AC
A
C
meets
Γ
\Gamma
Γ
at
E
E
E
. Prove that if
A
B
=
D
E
,
∠
A
C
B
=
6
0
∘
AB=DE, \angle{ACB}=60^{\circ}
A
B
=
D
E
,
∠
A
CB
=
6
0
∘
(sorry it is from my memory I can't remember the exact problem, but it means the same)
geometry
altitudes