MathDB

Bosnia and Herzegovina TST 1999 Day 2 Problem 1

Source: Bosnia and Herzegovina Team Selection Test 1999

September 20, 2018

geometryangle bisectorparallel

Problem Statement

Let angle bisectors of angles

\angle BAC

and

\angle ABC

of triangle

ABC

intersect sides

BC

and

AC

in points

D

and

E

, respectively. Let points

F

and

G

be foots of perpendiculars from point

C

on lines

AD

and

BE

, respectively. Prove that

FG \mid \mid AB