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Language: English Day: 1 49th INTERNATIONAL MATHEMATICAL OLYMPIAD MADRID (SPAIN), JULY 10-22, 2008 Wednesday, July 16, 2008 Problem 1. An acute-angled triangle ABC has orthocentre H. The circle passing through H with centre the midpoint of BC intersects the line BC at A1 and A2 . Similarly, the circle passing through H with centre the midpoint of CA intersects the line CA at B1 and B2 , and the circle passing through H with centre the midpoint of AB intersects the line AB at C1 and C2 .

- "Rock & Roll Suicide", Hammersmith Odeon, 1973 : Les concerts du Ziggy qu’incarnait Bowie sur scène relevaient plus de la performance que du simple concert. Pour passer l’épreuve de la scène, Bowie s’entoura de Mick Ronson à la guitare, Trevor Bolder à la basse et de Mick Woodmansey à la batterie. Tous trois bons musiciens, ils apportèrent une nouvelle dimension à l’album. Mick Ronson avait suivi une formation classique. Leader des Spiders From Mars, il était un excellent guitariste, dont Bowie

discussions in which each participant was randomly assigned fi�een-minute blocks of time during which he or she could comment on any aspect of what this new library might look like. No visual or written presentations were allowed, no flip charts or blackboards were available, and no one was allowed to use or take notes of any kind. The initial goal, which proved to be by far the most difficult part of the work, was to define the basic concept of a truly new academic library for EBU and the twenty-first

proposition II.6 is being interpreted more in the ‘algebraic’ sense referred to above. If this was done by the ancient Greeks, or by any of their successors, they were much more discreet about it than abu K¯ mil. a However, what abu K¯ mil did next was even bolder, as an innovation. Again, it may arise from the a study of Euclid, in this case of his book X; but this is not made clear, and the language is completely different. He develops a set of rules—not complete, but useful—for calculating with roots, and