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Mathley Magazine
Geometry Mathley 2011-12
15.2
15.2
Part of
Geometry Mathley 2011-12
Problems
(1)
Geometry Mathley 15.2 concyclic
Source:
6/13/2020
Let
O
O
O
be the centre of the circumcircle of triangle
A
B
C
ABC
A
BC
. Point
D
D
D
is on the side
B
C
BC
BC
. Let
(
K
)
(K)
(
K
)
be the circumcircle of
A
B
D
ABD
A
B
D
.
(
K
)
(K)
(
K
)
meets
A
O
AO
A
O
at
E
E
E
that is distinct from
A
A
A
. (a) Prove that
B
,
K
,
O
,
E
B,K,O,E
B
,
K
,
O
,
E
are on the same circle that is called
(
L
)
(L)
(
L
)
. (b)
(
L
)
(L)
(
L
)
intersects
A
B
AB
A
B
at
F
F
F
distinct
B
B
B
. Point
G
G
G
is on
(
L
)
(L)
(
L
)
such that
E
G
∥
O
F
EG \parallel OF
EG
∥
OF
.
G
K
GK
G
K
meets
A
D
AD
A
D
at
S
,
S
O
S, SO
S
,
SO
meets
B
C
BC
BC
at
T
T
T
. Prove that
O
,
E
,
T
,
C
O,E, T,C
O
,
E
,
T
,
C
are on the same circle.Trần Quang Hùng
geometry
Concyclic