MathDB
Problems
Contests
National and Regional Contests
Bangladesh Contests
Bangladesh Mathematical Olympiad
2024 Bangladesh Mathematical Olympiad
P2
P2
Part of
2024 Bangladesh Mathematical Olympiad
Problems
(1)
Four points on a circle
Source: BdMO 2024 Secondary National P2
3/18/2024
In a cyclic quadrilateral
A
B
C
D
ABCD
A
BC
D
, the diagonals intersect at
E
E
E
.
F
F
F
and
G
G
G
are on chord
A
C
AC
A
C
and chord
B
D
BD
B
D
respectively such that
A
F
=
B
E
AF = BE
A
F
=
BE
and
D
G
=
C
E
DG = CE
D
G
=
CE
. Prove that,
A
,
G
,
F
,
D
A, G, F, D
A
,
G
,
F
,
D
lie on the same circle.
geometry
cyclic quadrilateral
power of a point