MathDB

Points

E, F

are in the plane of triangle

ABC

so that triangles

ABE

and

ACF

are the opposite directed, and the two triangles are isosceles in that

BE = AE, AF = CF

. Let

H, K

be the orthocenter of triangle

ABE, ACF

respectively. Points

M, N

are the intersections of

BE

and

CF, CK

and

CH

. Prove that

MN

passes through the center of the circumcircle of triangle

ABC

.
Nguyen Minh Ha, High School for Education, Hanoi Pedagogical University

Problem Statement