MathDB

Three points aligned imply an isosceles triangle

Source: 38th Brazilian MO (2016) - First Day, Problem 1

November 23, 2016

geometryincenterParallel LinesBrazilian Math Olympiad 2016

Problem Statement

Let

ABC

be a triangle.

r

and

s

are the angle bisectors of

\angle ABC

and

\angle BCA

, respectively. The points

E

r

and

D

s

are such that

AD \| BE

and

AE \| CD

. The lines

BD

and

CE

cut each other at

F

I

is the incenter of

ABC

.
Show that if

A,F,I

are collinear, then

AB=AC