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Contests
National and Regional Contests
Korea Contests
Korea Junior Mathematics Olympiad
2001 Korea Junior Math Olympiad
8
8
Part of
2001 Korea Junior Math Olympiad
Problems
(1)
2001 KJMO P8 distance between a line and a point
Source: 2001 KJMO
6/29/2024
A
B
C
D
ABCD
A
BC
D
is a convex quadrilateral, both
∠
A
B
C
\angle ABC
∠
A
BC
and
∠
B
C
D
\angle BCD
∠
BC
D
acute.
E
E
E
is a point inside
A
B
C
D
ABCD
A
BC
D
satisfying
A
E
=
D
E
AE=DE
A
E
=
D
E
, and
X
,
Y
X, Y
X
,
Y
are the intersection of
A
D
AD
A
D
and
C
E
,
B
E
CE, BE
CE
,
BE
respectively, but not
X
=
A
X=A
X
=
A
or
Y
=
D
Y=D
Y
=
D
. If
A
B
E
X
ABEX
A
BEX
and
C
D
E
Y
CDEY
C
D
E
Y
are both inscribed quadrilaterals, prove that the distance between
E
E
E
and the lines
A
B
,
B
C
,
C
D
AB, BC, CD
A
B
,
BC
,
C
D
are all equal.
geometry
Concyclic