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Problems
Contests
National and Regional Contests
India Contests
India Pre-Regional Mathematical Olympiad
2013 India PRMO
12
12
Part of
2013 India PRMO
Problems
(1)
2013 preRMO p12, computational with equilateral and rectangle
Source:
8/8/2019
Let
A
B
C
ABC
A
BC
be an equilateral triangle. Let
P
P
P
and
S
S
S
be points on
A
B
AB
A
B
and
A
C
AC
A
C
, respectively, and let
Q
Q
Q
and
R
R
R
be points on
B
C
BC
BC
such that
P
Q
R
S
PQRS
PQRS
is a rectangle. If
P
Q
=
3
P
S
PQ = \sqrt3 PS
PQ
=
3
PS
and the area of
P
Q
R
S
PQRS
PQRS
is
28
3
28\sqrt3
28
3
, what is the length of
P
C
PC
PC
?
geometry
rectangle
Equilateral