MathDB
Problems
Contests
National and Regional Contests
Nigeria Contests
Nigerian Senior Mathematics Olympiad Round 3
2021 Nigerian MO Round 3
Problem 2
Problem 2
Part of
2021 Nigerian MO Round 3
Problems
(1)
Cyclic quads and collinear points
Source: 2021 Nigerian MO Round 3/P2
12/19/2022
Let
B
,
C
,
D
,
E
B, C, D, E
B
,
C
,
D
,
E
be four pairwise distinct collinear points and let
A
A
A
be a point not on ine
B
C
BC
BC
. Now, let the circumcircle of
△
A
B
C
\triangle ABC
△
A
BC
meet
A
D
AD
A
D
and
A
E
AE
A
E
respectively again at
F
F
F
and
G
G
G
. Show that
D
E
F
G
DEFG
D
EFG
is cyclic if and only if
A
B
=
A
C
AB=AC
A
B
=
A
C
.
geometry
Cyclic Quadrilaterals