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D belongs to the angle bisector of <AGF

Source: 2004 Bosnia & Herzegovina JBMO TST p5

May 27, 2020

isoscelesangle bisectorgeometry

Problem Statement

In the isosceles triangle

ABC

(

AC = BC

),

BC

and the altitude

CD =\sqrt2

. Let

E

and

F

be the midpoints of

BC

and

DB

, respectively and

G

be the intersection of

AE

and

CF

. Prove that

D

belongs to the angle bisector of

\angle AGF

.

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