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• 1993 AIME Problems/Problem 13
  ...math>P</math> and <math>Q</math> be the points of tangency of circle <math>O</math> to <math>AC</math> and <math>BD</math> respectively. pair A,B,C,D,P,Q,O,X;
  8 KB (1,231 words) - 20:06, 26 November 2023
• 1994 AIME Problems/Problem 8
  ...Thus, <math>M=\left(\frac{a+b}{2}, 24\right)</math>. The vector from <math>O</math> to <math>M</math> is <math>\left[\frac{a+b}{2}, 24\right]</math>. Me
  5 KB (788 words) - 13:53, 8 July 2023
• 1994 AIME Problems/Problem 2
  Call the center of the larger circle <math>O</math>. Extend the diameter <math>\overline{PQ}</math> to the other side of
  2 KB (272 words) - 03:53, 23 January 2023
• 1995 AIME Problems/Problem 14
  Let the center of the circle be <math>O</math>, and the two chords be <math>\overline{AB}, \overline{CD}</math> and ...pi/6), D=E+48*expi(7*pi/6), A=E+30*expi(5*pi/6), C=E+30*expi(pi/6), F=foot(O,B,A);
  3 KB (484 words) - 13:11, 14 January 2023
• 1995 AIME Problems/Problem 12
  triple A, B, C, D, O, P; O = (0,0,sqrt(2*sqrt(2)));
  8 KB (1,172 words) - 21:57, 22 September 2022
• 1996 AIME Problems/Problem 15
  In [[parallelogram]] <math>ABCD</math>, let <math>O</math> be the intersection of [[diagonal]]s <math>\overline{AC}</math> and pair B=(0,0), A=expi(pi/4), C=IP(A--A + 2*expi(17*pi/12), B--(3,0)), D=A+C, O=IP(A--C,B--D);
  5 KB (710 words) - 21:04, 14 September 2020
• 1996 AIME Problems/Problem 7
  pathpen = black; pair O = (3.5,3.5); D(O); D(arc(O,1,280,350),EndArrow(4));
  4 KB (551 words) - 11:44, 26 June 2020
• 1996 AIME Problems/Problem 4
  triple O=(0,0,0), P=(0,0,unit+unit/(r-1)); dot(P); draw(O--P); draw(O--(unit,0,0)--(unit,0,unit)--(0,0,unit)); draw(O--(0,unit,0)--(0,unit,unit)--(0,0,unit));
  2 KB (257 words) - 17:50, 4 January 2016
• 1997 AIME Problems/Problem 15
  ...math>AE=s</math> and thus circumradius <math>\frac{s}{2}</math>. Let <math>O</math> be its circumcenter. By Inscribed Angles, <math>\angle{BOD'}=2\angle
  4 KB (609 words) - 22:49, 17 July 2023
• 1997 AIME Problems/Problem 11
  Consider the rhombus <math>OABC</math> on the complex plane such that <math>O</math> is the origin, <math>A</math> represents <math>\text{cis } n^\circ</
  10 KB (1,512 words) - 17:16, 18 June 2024
• 1998 AIME Problems/Problem 4
  Let <math>O</math> stand for an odd number and <math>E</math> an even. ...<math>O</math>'s and the other two have two <math>E</math>'s and an <math>O</math> in them, respectively.) . Let's do the case <math>OOO</math>, <math>
  5 KB (917 words) - 02:37, 12 December 2022
• 1999 AIME Problems/Problem 15
  ...ely. Suppose <math>P</math> is the apex of the tetrahedron, and let <math>O</math> be the foot of the altitude from <math>P</math> to <math>\triangle A <b>Lemma:</b> The point <math>O</math> is the orthocenter of <math>\triangle ABC</math>.
  7 KB (1,169 words) - 15:28, 13 May 2024
• 1999 AIME Problems/Problem 4
  pair W=dir(225), X=dir(315), Y=dir(45), Z=dir(135), O=origin; dot(O);
  3 KB (398 words) - 13:27, 12 December 2020
• 2000 AIME I Problems/Problem 13
  Let the intersection of the highways be at the origin <math>O</math>, and let the highways be the x and y axes. We consider the case wher pair O=(0,0), B=(5,0), A=1.4*expi(atan(24/7)), C=1.4*expi(atan(7/24));
  3 KB (571 words) - 00:38, 13 March 2014
• 2001 AIME I Problems/Problem 14
  ...'s because no three o's can be adjacent, but there can be a maximum of two o's placed on the very left or right. Note that according to the [[Pigeonhole ...ixed so we count the number of ways to insert <math>19 - 10 - 9 = 0</math> o's to <math>10+1 = 11</math> spots, or <math>\binom{11}{0} = 1</math>.
  13 KB (2,298 words) - 19:46, 9 July 2020
• 2014 USAJMO Problems
  ...lateral, acute triangle with <math>\angle A=60^\circ</math>, and let <math>O</math> and <math>H</math> denote the circumcenter and orthocenter of <math>
  3 KB (600 words) - 16:42, 5 August 2023
• 2003 AIME I Problems/Problem 7
  pair O=(0,0),A=(-15,0),B=(-6,0),C=(15,0),D=(0,8);
  3 KB (490 words) - 18:13, 13 February 2021
• 2002 AIME II Problems/Problem 15
  pair[] O; O[1] = (r[1]/(2/3*sqrt(17/13)),r[1]);
  7 KB (1,188 words) - 17:46, 23 June 2024
• 2002 AIME II Problems/Problem 14
  ...ight angle]]. A [[circle]] of [[radius]] <math>19</math> with center <math>O</math> on <math>\overline{AP}</math> is drawn so that it is [[Tangent (geom Now use similarity, draw perpendicular from <math>O</math> to <math>PM</math>, name the new point <math>D</math>. Triangle <mat
  4 KB (658 words) - 19:15, 19 December 2021
• 2002 AIME II Problems/Problem 12
  Using X to represent a basket and O to represent a failure, this 'earliest' solution may be represented as:
  7 KB (1,127 words) - 13:34, 19 June 2022

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