MathDB

1

Part of 2023 Mexican Girls' Contest

Problems(2)

pages of an encyclopedia

Source: 2nd National Women´s Contest of Mexican Mathematics Olympiad 2023 , level 1 p1

7/23/2023
Gabriela found an encyclopedia with 20232023 pages, numbered from 11 to 20232023. She noticed that the pages formed only by even digits have a blue mark, and that every three pages since page two have a red mark. How many pages of the encyclopedia have both colors?
Mexico
geometry in a isosceles

Source: 2nd National Women´s Contest of Mexican Mathematics Olympiad 2023 , problem 1 teams

7/23/2023
Let △ABC\triangle ABC such that AB=ACAB=AC, DD and EE points on ABAB and BCBC, respectively, with DE∥ACDE\parallel AC. Let FF on line DEDE such that CADFCADF it´s a parallelogram. If OO is the circumcenter of △BDE\triangle BDE, prove that O,F,AO,F,A and DD lie on a circle.
geometryisoscelesMexico