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Show that two lines are perpendicular

Source: Turkey JBMO TST 2016 P5

May 22, 2016

geometry proposedperpendicular linesgeometry

Problem Statement

In an acute triangle

ABC

, the feet of the perpendiculars from

D

and

AB

to the opposite sides are

D

and

E

, respectively. The line passing through

E

and parallel to

BC

intersects

AC

at

F

, the line passing through

D

and parallel to

AB

intersects

AC

at

G

. The feet of the perpendiculars from

F

to

DG

and

GE

are

K

and

L

, respectively.

KL

intersects

ED

at

M

. Prove that

FM \perp ED

.

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