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2014 Lusophon Mathematical Olympiad
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Part of
2014 Lusophon Mathematical Olympiad
Problems
(1)
IV Lusophon Mathematical Olympiad 2014 - Problem 3
Source:
12/28/2014
In a convex quadrilateral
A
B
C
D
ABCD
A
BC
D
,
P
P
P
and
Q
Q
Q
are points on sides
B
C
BC
BC
and
D
C
DC
D
C
such that
B
A
^
P
=
D
A
^
Q
B\hat{A}P = D\hat{A}Q
B
A
^
P
=
D
A
^
Q
. If the line that passes through the orthocenters of
△
A
B
P
\triangle ABP
△
A
BP
and
△
A
D
Q
\triangle ADQ
△
A
D
Q
is perpendicular to
A
C
AC
A
C
, prove that the area of these triangles are equals.
geometry