MathDB

altitude and circumcircles

Source: 3rd National Women´s Contest of Mexican Mathematics Olympiad 2024 , level 1+2 p3

June 13, 2024

geometryMexicocircumcircle

Problem Statement

Let

ABC

be a triangle and

D

the foot of the altitude from

A

. Let

M

be a point such that

MB = MC

. Let

E

and

F

be the intersections of the circumcircle of

BMD

and

CMD

with

AD

. Let

G

and

H

be the intersections of

MB

and

MC

with

AD

. Prove that

EG = FH