MathDB

IMEO 2017 Problem 2

Source: IMEO

September 28, 2017

geometryJunior

Problem Statement

Let

O

be the circumcenter of a triangle

ABC

. Let

M

be the midpoint of

AO

. The

BO

and

CO

intersect the altitude

AD

at points

E

and

F

,respectively. Let

O1

and

O2

be the circumcenters of the triangle ABE and

ACF

, respectively. Prove that M lies on

O1O2

.

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