MathDB

Nice triangular similarity problem in the Centro

Source: Centroamerican and Caribbean Math Olympiad 2024 P4

October 18, 2024

geometrysimilaritycircumcircleincenter

Problem Statement

Let

ABC

be a triangle,

I

its incenter, and

\Gamma

its circumcircle. Let

D

be the second point of intersection of

AI

with

\Gamma

. The line parallel to

BC

through

I

intersects

AB

and

AC

P

and

Q

, respectively. The lines

PD

and

QD

intersect

BC

E

and

F

, respectively. Prove that triangles

IEF

and

ABC

are similar.