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AF _|_ DE wanted, projections on external angle bisectors

Source: Czech-Polish-Slovak Match Junior 2021, individual p2 CPSJ

September 12, 2021

perpendicularangle bisectorgeometry

Problem Statement

An acute triangle

ABC

is given. Let us denote by

D

and

E

the orthogonal projections, respectively of points

B

and

C

on the bisector of the external angle

BAC

. Let

F

be the point of intersection of the lines

BE

and

CD

. Show that the lines

AF

and

DE

are perpendicular.