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isosceles

Source: Taiwan 2nd TST 2005, 2nd independent study, problem 2

August 12, 2005

geometryparallelogramrhombusgeometry proposed

Problem Statement

It is known that

\triangle ABC

is an acute triangle. Let

C'

be the foott of the perpendicular from

C

to

AB

, and

D

,

E

two distinct points on

CC'

. The feet of the perpendiculars from

D

to

AC

and

BC

are

F

and

G

, respectively. Show that if

DGEF

is a parallelogram then

ABC

is isosceles.

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