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National and Regional Contests
India Contests
India Pre-Regional Mathematical Olympiad
2016 India PRMO
5
5
Part of
2016 India PRMO
Problems
(1)
2016 preRMO p5, line perpendicular to BC bisects triangle's area
Source:
8/9/2019
Consider a triangle
A
B
C
ABC
A
BC
with
A
B
=
13
,
B
C
=
14
,
C
A
=
15
AB = 13, BC = 14, CA = 15
A
B
=
13
,
BC
=
14
,
C
A
=
15
. A line perpendicular to
B
C
BC
BC
divides the interior of
△
B
C
\vartriangle BC
△
BC
into two regions of equal area. Suppose that the aforesaid perpendicular cuts
B
C
BC
BC
at
D
D
D
, and cuts
△
A
B
C
\vartriangle ABC
△
A
BC
again at
E
E
E
. If
L
L
L
is the length of the line segment
D
E
DE
D
E
, find
L
2
L^2
L
2
.
geometry
areas