MathDB

Circumcenters

Source: Czech and Slovak Olympiad 2018, National Round, Problem 3

April 5, 2018

geometrynational olympiadcircumcircle

Problem Statement

In triangle

ABC

let be

D

an intersection of

BC

and the

A

-angle bisector. Denote

E,F

the circumcenters of

ABD

and

ACD

respectively. Assuming that the circumcenter of

AEF

lies on the line

BC

what is the possible size of the angle

BAC