MathDB

1

Part of 2017 Regional Olympiad of Mexico Southeast

Problems(1)

Prove a point is fixed

Source: Mathematics Regional Olympiad of Mexico Southeast 2017 P1

10/24/2021
Let ABCABC a triangle and CC it´s circuncircle. Let DD a point in arc ABAB that not contain AA, diferent of BB and CC such that CDCD and ABAB are not parallel. Let EE the intersection of CDCD and ABAB and OO the circumcircle of triangle DBEDBE. Prove that the measure of ∠OBE\angle OBE does not depend of the choice of DD.
geometrycircumcircle