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Turkey Team Selection Test
2020 Turkey Team Selection Test
6
6
Part of
2020 Turkey Team Selection Test
Problems
(1)
p6 geometry
Source: Turkey TST 2020 Day 2 P6
3/10/2020
In a triangle
△
A
B
C
\triangle ABC
△
A
BC
,
D
D
D
and
E
E
E
are respectively on
A
B
AB
A
B
and
A
C
AC
A
C
such that
D
E
∥
B
C
DE\parallel BC
D
E
∥
BC
.
P
P
P
is the intersection of
B
E
BE
BE
and
C
D
CD
C
D
.
M
M
M
is the second intersection of
(
A
P
D
)
(APD)
(
A
P
D
)
and
(
B
C
D
)
(BCD)
(
BC
D
)
,
N
N
N
is the second intersection of
(
A
P
E
)
(APE)
(
A
PE
)
and
(
B
C
E
)
(BCE)
(
BCE
)
.
w
w
w
is the circle passing through
M
M
M
and
N
N
N
and tangent to
B
C
BC
BC
. Prove that the lines tangent to
w
w
w
at
M
M
M
and
N
N
N
intersect on
A
P
AP
A
P
.
geometry