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2023 Pan-African
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PAMO 2023 Problem 1
Source: 2023 Pan African Mathematics Olympaid, Problem 1
5/17/2023
In a triangle
A
B
C
ABC
A
BC
with
A
B
<
A
C
AB<AC
A
B
<
A
C
,
D
D
D
is a point on segment
A
C
AC
A
C
such that
B
D
=
C
D
BD = CD
B
D
=
C
D
. A line parallel to
B
D
BD
B
D
meets segment
B
C
BC
BC
at
E
E
E
and line
A
B
AB
A
B
at
F
F
F
. Point
G
G
G
is the intersection of
A
E
AE
A
E
and
B
D
BD
B
D
. Show that
∠
B
C
G
=
∠
B
C
F
\angle BCG = \angle BCF
∠
BCG
=
∠
BCF
. (Côte d’Ivoire)
PAMO
geometry