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Contests
National and Regional Contests
India Contests
India Pre-Regional Mathematical Olympiad
2013 India PRMO
19
19
Part of
2013 India PRMO
Problems
(1)
2013 preRMO p19, computational with right triangle and ratio of areas
Source:
8/8/2019
In a triangle
A
B
C
ABC
A
BC
with
∠
B
C
A
=
9
0
o
\angle BC A = 90^o
∠
BC
A
=
9
0
o
, the perpendicular bisector of
A
B
AB
A
B
intersects segments
A
B
AB
A
B
and
A
C
AC
A
C
at
X
X
X
and
Y
Y
Y
, respectively. If the ratio of the area of quadrilateral
B
X
Y
C
BXYC
BX
Y
C
to the area of triangle
A
B
C
ABC
A
BC
is
13
:
18
13 : 18
13
:
18
and
B
C
=
12
BC = 12
BC
=
12
then what is the length of
A
C
AC
A
C
?
ratio
areas
right triangle