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• 1989 AJHSME Problems/Problem 10
  ...le]] between the hour hand and the minute hand on a clock that reads seven o'clock?
  683 bytes (100 words) - 23:57, 4 July 2013
• 1989 AJHSME Problems/Problem 19
  label("S",(8.5,0),S); label("O",(9.5,0),S); label("N",(10.5,0),S); label("D",(11.5,0),S);
  2 KB (255 words) - 03:28, 28 November 2019
• 1990 AJHSME Problems/Problem 19
  Let <math>p</math> be a person seated and <math>o</math> is an empty seat
  727 bytes (119 words) - 01:59, 25 November 2020
• 1965 IMO Problems
  ...OAB</math> with acute angle <math>AOB</math>. Through a point <math>M \neq O</math> perpendiculars are drawn to <math>OA</math> and <math>OB</math>, the
  3 KB (497 words) - 12:39, 29 January 2021
• 1965 IMO Problems/Problem 5
  ...OAB</math> with acute angle <math>AOB</math>. Through a point <math>M \neq O</math> perpendiculars are drawn to <math>OA</math> and <math>OB</math>, the Let <math>O(0,0),A(a,0),B(b,c)</math>.
  1 KB (269 words) - 00:23, 9 December 2022
• 2009 IMO Problems/Problem 2
  Let <math>ABC</math> be a triangle with circumcentre <math>O</math>. The points <math>P</math> and <math>Q</math> are interior points of dot("O", (50, 38), N);
  2 KB (280 words) - 01:16, 19 November 2023
• 2009 IMO Problems
  Let <math>ABC</math> be a triangle with circumcentre <math>O</math>. The points <math>P</math> and <math>Q</math> are interior points of
  3 KB (509 words) - 09:23, 10 September 2020
• Schroeder-Bernstein Theorem
  ...there is an open interval <math>I</math> satisfying <math>r\in I\subseteq O</math>. Show that the following sets are equal in cardinality: *<math>\{O\subset\mathbb{R}\mid O\text{ is open}\}</math>
  4 KB (805 words) - 13:09, 20 February 2024
• 1992 AJHSME Problems
  label("O",(16.5,5.8),N);
  17 KB (2,346 words) - 13:36, 19 February 2020
• 2010 AMC 10B Problems
  A circle is centered at <math>O</math>, <math>\overline{AB}</math> is a diameter and <math>C</math> is a po ...th> is a chord on the circle, <math>OA = 4\sqrt{3}</math>, and point <math>O</math> is outside <math>\triangle ABC</math>. What is the side length of <m
  12 KB (1,817 words) - 22:44, 22 December 2020
• Characteristic polynomial
  ...\bold{T}^1 + v_2 \cdot \bold{T}^2 + \cdots + v_n \cdot \bold{T}^n = \bold{O}.</cmath> ...lambda \bold{v}</math>, then <math>\lambda I \bold{v} - A \bold{v} = \bold{O}</math>. But then, the column vectors of <math>\lambda I - A</math> are lin
  19 KB (3,412 words) - 14:57, 21 September 2022
• Linearly independent
  ...not all equal to zero such that <cmath>c_1v_1 + c_2v_2 + \cdots + c_nv_n = O.</cmath> Otherwise, the vectors are said to be [[linearly dependent]]. ...mbda_1c_iv_i = O,\qquad L\left(\sum c_iv_i\right) = \sum \lambda_ic_iv_i = O.</cmath> Subtracting the two equations yields <cmath>\sum (\lambda_1-\lambd
  2 KB (300 words) - 23:35, 16 March 2010
• 2010 AIME I Problems/Problem 13
  label("$O$",(129.36332,5.00321),NE/2); ...the semicircle is also the midpoint of <math>AB</math>. Let this point be O. Let <math>h</math> be the length of <math>AD</math>.
  10 KB (1,418 words) - 23:05, 20 October 2021
• Mock AIME 2 2010 Answer Key
  ...center of the circle, and let points E and F to be the perpendiculars from O to AC and BC, respectively. First, by power of a point, we have <math>CD \c We shall prove that in a circle <math>\mathcal{C}</math> with center <math>O</math>, radius <math>R</math>, a chord <math>BC</math> with midpoint <math>
  36 KB (6,214 words) - 20:22, 13 July 2023
• 2007 IMO Problems/Problem 1
  ...who is a horrible proof writer, so please fix the proof for me. Thank you. O, also the formatting.
  4 KB (768 words) - 23:15, 31 March 2010
• 2010 AIME II Problems/Problem 14
  Let <math>O</math> be the [[circumcenter]] of <math>ABC</math> and let the intersection Denote <math>E</math> the projection of <math>O</math> onto <math>CD</math>. Now <math>CD = CP + DP = 3</math>. By the [[Py
  10 KB (1,507 words) - 00:31, 19 November 2023
• 2010 AIME II Problems/Problem 9
  pair M,N,O,P,Q,R; O=extension(C,J,D,K);
  5 KB (857 words) - 22:22, 27 August 2023
• 2010 AIME II Problems/Problem 11
  ...ac-toe board: five <math>1</math>'s (or X's) and four <math>0</math>'s (or O's).
  6 KB (1,057 words) - 01:58, 8 January 2023
• 2010 USAMO Problems
  ...d <math>RS</math> is half the size of <math>\angle XOZ</math>, where <math>O</math> is the midpoint of segment <math>AB</math>.
  3 KB (525 words) - 13:44, 4 July 2013
• 2010 USAJMO Problems
  ...d <math>RS</math> is half the size of <math>\angle XOZ</math>, where <math>O</math> is the midpoint of segment <math>AB</math>.
  3 KB (538 words) - 13:55, 16 June 2020

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