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Sweden Contests
Swedish Mathematical Competition
1990 Swedish Mathematical Competition
4
4
Part of
1990 Swedish Mathematical Competition
Problems
(1)
LM = AL + BM wanted, angle bisectors, ABCD
Source: 1990 Swedish Mathematical Competition p4
4/2/2021
A
B
C
D
ABCD
A
BC
D
is a quadrilateral. The bisectors of
∠
A
\angle A
∠
A
and
∠
B
\angle B
∠
B
meet at
E
E
E
. The line through
E
E
E
parallel to
C
D
CD
C
D
meets
A
D
AD
A
D
at
L
L
L
and
B
C
BC
BC
at
M
M
M
. Show that
L
M
=
A
L
+
B
M
LM = AL + BM
L
M
=
A
L
+
BM
.
geometry
angle bisector
equal segments