Problem: Let $ABC$ be an acute triangle. Let $D$ be the foot of the altitude from $A$. Prove that if $AB + BD = AC + CD$, then $AB = AC$. Solution Sketch: This requires constructing a circle or using reflection properties to show the symmetry of the triangle based on the condition of the sum of side lengths.
Subject: History, Structure, Problems, and Resources Date: October 26, 2023 cuban mathematical olympiads pdf
Since all documents are in Spanish, non-native speakers have two options. However, the mathematical notation is universal. A "Cuban mathematical olympiads pdf" is valuable even if you don't speak Spanish because: Problem: Let $ABC$ be an acute triangle
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To give you a taste of what you will find in a typical resource, here are three sample problems often featured in Cuban MO collections.
Problem: In a chess tournament, each player plays every other player exactly once. A player gets 1 point for a win, 0.5 for a draw, and 0 for a loss. If the total number of players is $n$ and the sum of the points of all players is $T$, determine the maximum possible score for the winner.