MathDB

(con)cyclic wanted, projections of vertices on medians related

Source: 2014 Saudi Arabia GMO TST day I p1

July 31, 2020

ConcyclicgeometryCyclicMedians

Problem Statement

Let

ABC

be a triangle with

\angle A < \angle B \le \angle C

M

and

N

the midpoints of sides

CA

and

AB

, respectively, and

P

and

Q

the projections of

B

and

C

on the medians

CN

and

BM

, respectively. Prove that the quadrilateral

MNPQ

is cyclic.