MathDB

2024 BxMO P3

Source: 2024 BxMO P3

April 28, 2024

geometry

Problem Statement

Let

ABC

be a triangle with incentre

I

and circumcircle

\Omega

such that

\left|AC\right|\neq\left|BC\right|

. The internal angle bisector of

\angle CAB

intersects side

BC

at

D

and the external angle bisectors of

\angle ABC

and

\angle BCA

intersect

\Omega

at

E

and

F

respectively. Let

G

be the intersection of lines

AE

and

FI

and let

\Gamma

be the circumcircle of triangle

BDI

. Show that

E

lies on

\Gamma

if and only if

G

lies on

\Gamma

.

Back to Problems View on AoPS