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  • === Solution 8 (Ratios, Auxiliary Lines and 3-4-5 triangle) ===
    14 KB (2,234 words) - 15:31, 22 December 2024
  • Using [[homothety]] in the diagram above, as well as the [[auxiliary]] triangle, leads to the solution.
    11 KB (1,853 words) - 19:10, 21 July 2024
  • We reduce the problem to [[Rolle's theorem]] by using an auxiliary function.
    1 KB (210 words) - 11:53, 20 February 2024
  • We find an auxiliary point <math>S.</math>
    5 KB (792 words) - 00:52, 19 November 2023
  • | A reference to the current picture. Used as an auxiliary command in other commands. This is the default value, so it is used only in
    21 KB (3,334 words) - 22:53, 23 March 2022
  • Draw the auxiliary line <math>AC</math>. Denote by <math>M</math> the point it intersects with
    12 KB (2,059 words) - 16:52, 3 November 2024
  • ==Solution 7 (Intuitive, no trig, no weird auxiliary lines)==
    17 KB (2,753 words) - 13:30, 8 December 2024
  • First, let's draw a few auxiliary lines. Drop altitudes from <math>O</math> to <math>AB</math> and from <math
    3 KB (445 words) - 09:43, 20 April 2021
  • ...icular from <math>M</math> to <math>\overline{KL}.</math> We construct the auxiliary lines, as shown below:
    3 KB (462 words) - 06:58, 6 September 2021
  • ...ntered in the preparation classes for the Olympiad, specifically involving auxiliary sets and functions with specific properties.
    4 KB (657 words) - 11:41, 20 December 2023
  • Elites-Low ranking officers, elite units, or specialized auxiliary units, depending on the army. Auxiliary: 1 Warlord or 0-10 Troops or 0-10 Elites or 0-4 Cavalry or 1 Heavy Support
    36 KB (5,897 words) - 18:28, 3 September 2024
  • ==Solution 2 (Auxiliary Lines)==
    7 KB (1,170 words) - 04:47, 5 November 2024
  • ...This implies f(x)>0 for all x>0, allowing us to define an auxiliary function g as g(x)=f(x).
    2 KB (369 words) - 15:12, 26 March 2024