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LM = AL + BM wanted, angle bisectors, ABCD

Source: 1990 Swedish Mathematical Competition p4

April 2, 2021

geometryangle bisectorequal segments

Problem Statement

ABCD

is a quadrilateral. The bisectors of

\angle A

and

\angle B

meet at

E

. The line through

E

parallel to

CD

meets

AD

at

L

and

BC

at

M

. Show that

LM = AL + BM

.

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