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Mathley Magazine
Geometry Mathley 2011-12
11.2
11.2
Part of
Geometry Mathley 2011-12
Problems
(1)
Geometry Mathley 11.2 AP = AQ , BM = BC = CN
Source:
6/7/2020
Let
A
B
C
ABC
A
BC
be a triangle inscribed in the circle
(
O
)
(O)
(
O
)
. Tangents at
B
,
C
B,C
B
,
C
of the circles
(
O
)
(O)
(
O
)
meet at
T
T
T
. Let
M
,
N
M,N
M
,
N
be the points on the rays
B
T
,
C
T
BT,CT
BT
,
CT
respectively such that
B
M
=
B
C
=
C
N
BM = BC = CN
BM
=
BC
=
CN
. The line through
M
M
M
and
N
N
N
intersects
C
A
,
A
B
CA,AB
C
A
,
A
B
at
E
,
F
E, F
E
,
F
respectively;
B
E
BE
BE
meets
C
T
CT
CT
at
P
,
C
F
P, CF
P
,
CF
intersects
B
T
BT
BT
at
Q
Q
Q
. Prove that
A
P
=
A
Q
AP = AQ
A
P
=
A
Q
.Trần Quang Hùng
geometry
equal segments