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Problems
Contests
National and Regional Contests
India Contests
India Pre-Regional Mathematical Olympiad
2017 India PRMO
24
24
Part of
2017 India PRMO
Problems
(1)
Geometry
Source: PRMO 2017
9/16/2017
Let
P
P
P
be an interior point of a triangle
A
B
C
ABC
A
BC
whose sidelengths are 26, 65, 78. The line through
P
P
P
parallel to
B
C
BC
BC
meets
A
B
AB
A
B
in
K
K
K
and
A
C
AC
A
C
in
L
L
L
. The line through
P
P
P
parallel to
C
A
CA
C
A
meets
B
C
BC
BC
in
M
M
M
and
B
A
BA
B
A
in
N
N
N
. The line through
P
P
P
parallel to
A
B
AB
A
B
meets
C
A
CA
C
A
in
S
S
S
and
C
B
CB
CB
in
T
T
T
. If
K
L
,
M
N
,
S
T
KL,MN,ST
K
L
,
MN
,
ST
are of equal lengths, find this common length.
geometry