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Geometry problem about ABC and its circumcircle

Source: Turkey Junior Math Olympiad #3 Problem

January 19, 2019

geometrycircumcircleTurkeyJunior

Problem Statement

In an acute

ABC

triangle which has a circumcircle center called

O

, there is a line that perpendiculars to

AO

line cuts

[AB]

and

[AC]

respectively on

D

and

E

points. There is a point called

K

that is different from

AO

and

BC

's junction point on

[BC]

.

AK

line cuts the circumcircle of

ADE

on

L

that is different from

A

.

M

is the symmetry point of

A

according to

DE

line. Prove that

K

,

L

,

M

,

O

are circular.

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