MathDB

Prove a point is fixed

Source: Mathematics Regional Olympiad of Mexico Southeast 2017 P1

October 24, 2021

geometrycircumcircle

Problem Statement

Let

ABC

a triangle and

C

it´s circuncircle. Let

D

a point in arc

AB

that not contain

A

, diferent of

B

and

C

such that

CD

and

AB

are not parallel. Let

E

the intersection of

CD

and

AB

and

O

the circumcircle of triangle

DBE

. Prove that the measure of

\angle OBE

does not depend of the choice of

D