MathDB

parallelism

Source: Netherlands TST for Bxmo 2017, problem 3

February 1, 2018

geometry

Problem Statement

Let

ABC

be a triangle with

\angle A = 90

and let

D

be the orthogonal projection of

A

onto

BC

. The midpoints of

AD

and

AC

are called

E

and

F

, respectively. Let

M

be the circumcentre of

BEF

. Prove that

AC

and

BM

are parallel.

Back to Problems View on AoPS