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Regional Mathematical Olympiad
1992 India Regional Mathematical Olympiad
5
Another simple one on quads
Another simple one on quads
Source: Indian RMO 1992 Problem 6
October 15, 2005
geometry
Problem Statement
A
B
C
D
ABCD
A
BC
D
is a quadrilateral and
P
,
Q
P,Q
P
,
Q
are the midpoints of
C
D
,
A
B
,
A
P
,
D
Q
CD, AB, AP, DQ
C
D
,
A
B
,
A
P
,
D
Q
meet at
X
X
X
and
B
P
,
C
Q
BP, CQ
BP
,
CQ
meet at
Y
Y
Y
. Prove that
A
[
A
D
X
]
+
A
[
B
C
Y
]
=
A
[
P
X
O
Y
]
A[ADX]+A[BCY] = A[PXOY]
A
[
A
D
X
]
+
A
[
BC
Y
]
=
A
[
PXO
Y
]
.
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