6

Part of 2011 CentroAmerican

Problems(1)

Orthic triangle DEF satisfying 3EF=FD+DE

Source: Centroamerican 2011, Problem 6

ABC

be an acute triangle and

D

E

F

be the feet of the altitudes through

DE

B

C

respectively. Call

Y

Z

the feet of the perpendicular lines from

B

C

FD

DE

, respectively. Let

F_1

be the symmetric of

F

with respect to

E

E_1

be the symmetric of

E

with respect to

F

3EF=FD+DE

\angle BZF_1=\angle CYE_1

trigonometrygeometryperpendicular bisectorgeometry proposed