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Contests
National and Regional Contests
India Contests
India Pre-Regional Mathematical Olympiad
2014 India PRMO
10
10
Part of
2014 India PRMO
Problems
(1)
2014 preRMO p10, computational with ratios and areas
Source:
8/9/2019
In a triangle
A
B
C
,
X
ABC, X
A
BC
,
X
and
Y
Y
Y
are points on the segments
A
B
AB
A
B
and
A
C
AC
A
C
, respectively, such that
A
X
:
X
B
=
1
:
2
AX : XB = 1 : 2
A
X
:
XB
=
1
:
2
and
A
Y
:
Y
C
=
2
:
1
AY :YC = 2:1
A
Y
:
Y
C
=
2
:
1
. If the area of triangle
A
X
Y
AXY
A
X
Y
is
10
10
10
, then what is the area of triangle
A
B
C
ABC
A
BC
?
ratio
geometry
areas