MathDB

Let

ABC

be a scalene triangle whose incircle is tangent to

BC

CA

AB

D

E

F

respectively. Lines

BE

and

CF

meet at

G

. Prove that there exists a point

X

on the circumcircle of triangle

EFG

such that the circumcircles of triangles

BCX

and

EFG

are tangent, and

\angle BGC = \angle BXC + \angle EDF.

Kornpholkrit Weraarchakul

Problem Statement