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Contests
National and Regional Contests
Korea Contests
Korea Summer Program Practice Test
2016 Korea Summer Program Practice Test
2
2
Part of
2016 Korea Summer Program Practice Test
Problems
(1)
Collinearity of three points
Source: Korean Summer Program Practice Test 2016 2
8/17/2016
Let the incircle of triangle
A
B
C
ABC
A
BC
meet the sides
B
C
BC
BC
,
C
A
CA
C
A
,
A
B
AB
A
B
at
D
D
D
,
E
E
E
,
F
F
F
, and let the
A
A
A
-excircle meet the lines
B
C
BC
BC
,
C
A
CA
C
A
,
A
B
AB
A
B
at
P
P
P
,
Q
Q
Q
,
R
R
R
. Let the line passing through
A
A
A
and perpendicular to
B
C
BC
BC
meet the lines
E
F
EF
EF
,
Q
R
QR
QR
at
K
K
K
,
L
L
L
. Let the intersection of
L
D
LD
L
D
and
E
F
EF
EF
be
S
S
S
, and the intersection of
K
P
KP
K
P
and
Q
R
QR
QR
be
T
T
T
. Prove that
A
A
A
,
S
S
S
,
T
T
T
are collinear.
geometry