MathDB
Problems
Contests
International Contests
Pan-African Shortlist
2018 Pan-African Shortlist
G6
G6
Part of
2018 Pan-African Shortlist
Problems
(1)
Arcs are equal in construction involving altitude and angle bisector
Source: 2018 Pan-African Shortlist - G6
5/7/2019
Let
Γ
\Gamma
Γ
be the circumcircle of an acute triangle
A
B
C
ABC
A
BC
. The perpendicular line to
A
B
AB
A
B
passing through
C
C
C
cuts
A
B
AB
A
B
in
D
D
D
and
Γ
\Gamma
Γ
again in
E
E
E
. The bisector of the angle
C
C
C
cuts
A
B
AB
A
B
in
F
F
F
and
Γ
\Gamma
Γ
again in
G
G
G
. The line
G
D
GD
G
D
meets
Γ
\Gamma
Γ
again at
H
H
H
and the line
H
F
HF
H
F
meets
Γ
\Gamma
Γ
again at
I
I
I
. Prove that
A
I
=
E
B
AI = EB
A
I
=
EB
.
geometry
angle bisector