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Canada Contests
Canadian Mathematical Olympiad Qualification Repechage
2022 Canadian Mathematical Olympiad Qualification
7
7
Part of
2022 Canadian Mathematical Olympiad Qualification
Problems
(1)
Chase your Dreams
Source: Canada Repechage 2022/7 CMOQR
3/19/2022
Let
A
B
C
ABC
A
BC
be a triangle with
∣
A
B
∣
<
∣
A
C
∣
|AB| < |AC|
∣
A
B
∣
<
∣
A
C
∣
, where
∣
⋅
∣
| · |
∣
⋅
∣
denotes length. Suppose
D
,
E
,
F
D, E, F
D
,
E
,
F
are points on side
B
C
BC
BC
such that
D
D
D
is the foot of the perpendicular on
B
C
BC
BC
from
A
A
A
,
A
E
AE
A
E
is the angle bisector of
∠
B
A
C
\angle BAC
∠
B
A
C
, and
F
F
F
is the midpoint of
B
C
BC
BC
. Further suppose that
∠
B
A
D
=
∠
D
A
E
=
∠
E
A
F
=
∠
F
A
C
\angle BAD = \angle DAE = \angle EAF = \angle FAC
∠
B
A
D
=
∠
D
A
E
=
∠
E
A
F
=
∠
F
A
C
. Determine all possible values of
∠
A
B
C
\angle ABC
∠
A
BC
.
geometry
Canada
repechage