MathDB

1

Part of 2011 Lusophon Mathematical Olympiad

Problems(2)

Circle Inscribed in a Hexagon

Source: 2011 LMO Problem #1

9/21/2011
Prove that the area of the circle inscribed in a regular hexagon is greater than 90%90\% of the area of the hexagon.
geometryratio
Logic

Source:

9/21/2011
Each one of three friends, Mário, João and Filipe, does one, and only one, of the following sports: football, basketball and swimming. None of these sports is done by more than one of the friends. Each one of the friends likes a certain kind of fruit: one likes oranges, another likes bananas and the other likes papayas. Find, for each one, which sport he plays and which fruit he prefers, given that:
* Mário doesn't like oranges;
* João doesn't play football;
* The swimmer hates bananas;
* The swimmer and the one who likes oranges do different sports;
* The one who likes papayas and the footballer visit Filipe every Saturday.