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Problems
Contests
National and Regional Contests
India Contests
India Pre-Regional Mathematical Olympiad
2014 India PRMO
15
15
Part of
2014 India PRMO
Problems
(1)
2014 preRMO p15, computational with right triangle and midpoints
Source:
8/9/2019
Let
X
O
Y
XOY
XO
Y
be a triangle with
∠
X
O
Y
=
9
0
o
\angle XOY = 90^o
∠
XO
Y
=
9
0
o
. Let
M
M
M
and
N
N
N
be the midpoints of legs
O
X
OX
OX
and
O
Y
OY
O
Y
, respectively. Suppose that
X
N
=
19
XN = 19
XN
=
19
and
Y
M
=
22
YM =22
Y
M
=
22
. What is
X
Y
XY
X
Y
?
geometry
midpoint
right triangle