MathDB

X, Y, O1, O2 are concyclic

Source: Serbia Math Olympiad 2011

April 8, 2011

geometrycircumcircleparallelogramgeometric transformationreflectiongeometry proposed

Problem Statement

On sides

AB, AC, BC

are points

M, X, Y

, respectively, such that

AX=MX

;

BY=MY

K

L

are midpoints of

AY

and

BX

O

is circumcenter of

ABC

O_1

O_2

are symmetric with

O

with respect to

K

and

L

. Prove that

X, Y, O_1, O_2

are concyclic.