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• 2018 AMC 12A Problems/Problem 20
  ...ac{9}{4}-\frac{3}{2}b</math>. Notice that <math>EI=2MO</math>, where <math>O</math> is the origin of the circle mentioned in the problem. Thus <math>\fr
  7 KB (1,218 words) - 04:03, 23 January 2023
• 2018 AMC 12B Problems
  ...h>AB = 13</math>, <math>AC = 12</math>, and <math>BC = 5</math>, let <math>O</math> and <math>I</math> denote the circumcenter and incenter, respectivel
  14 KB (2,118 words) - 15:36, 28 October 2021
• 2018 AMC 12B Problems/Problem 16
  ...re consecutive vertices of the octagon. By dropping an altitude from <math>O</math> to <math>AB</math>, note that <math>\frac{1}{2} AB = \sqrt{3} \sin(2
  11 KB (1,708 words) - 12:01, 18 March 2023
• 2018 AMC 12B Problems/Problem 21
  ...h>AB = 13</math>, <math>AC = 12</math>, and <math>BC = 5</math>, let <math>O</math> and <math>I</math> denote the circumcenter and incenter, respectivel pair A, B, C, O, I, M;
  3 KB (540 words) - 04:12, 30 August 2022
• 2018 AMC 10B Problems/Problem 12
  pair O, A, B, C1, C2, G1, G2, M1, M2; O = (0,0);
  4 KB (647 words) - 14:19, 5 June 2023
• 2018 AMC 10B Problems/Problem 24
  pair A, B, C, D, E, F, X, Y, Z, M, N, O, P, Q, R; O = intersectionpoint(C--E,Y--Z);
  17 KB (2,562 words) - 03:38, 6 September 2022
• 2018 AMC 12B Problems/Problem 4
  Let <math>O</math> be the center of the circle, <math>\overline{AB}</math> be the chord pair O, A, B, M;
  2 KB (244 words) - 22:06, 27 May 2023
• 1973 IMO Problems/Problem 1
  Point <math>O</math> lies on line <math>g;</math> <math>\overrightarrow{OP_1}, \overright
  1 KB (227 words) - 15:45, 29 January 2021
• 2016 JBMO Problems/Problem 3
  ...modular equation by 4, we get <math>1008^o\equiv 1\pmod {(4s+d_1)(sd_1)}, o=2n-1</math>. ...s that <math>o</math> is one less than that <math>p</math>. However, <math>o</math> must be odd so the only <math>p</math> that works is <math>p=2</math
  4 KB (639 words) - 15:14, 28 November 2023
• 1960 AHSME Problems/Problem 15
  pair A=(0,50),O=(0,0),B=(43.301,-25),C=(-43.301,-25); draw(circle(O,50));
  2 KB (276 words) - 19:01, 17 May 2018
• 1960 AHSME Problems/Problem 32
  In this figure the center of the circle is <math>O</math>. <math>AB \perp BC</math>, <math>ADOE</math> is a straight line, <ma pair O=origin,E=dir(e),C=dir(c),B=dir(180+c),D=dir(180+e), rot=rotate(90,B)*O,A=extension(E,D,B,rot);
  3 KB (508 words) - 20:33, 17 August 2022
• 1961 AHSME Problems/Problem 38
  ...eved when <math>CO</math> is perpendicular to <math>AB</math>, where <math>O</math> is the origin of the semicircle. We will prove this using the Mean I
  3 KB (545 words) - 04:29, 17 October 2022
• Olympiad Archive
  ** Problems w/o Solutions ** [https://bmos.ukmt.org.uk/home/bmo.shtml ''Problems since 1972 w/o Solutions'']
  16 KB (1,987 words) - 11:39, 17 February 2024
• 2018 AIME I Problems/Problem 10
  ...l going clockwise (because it has to be in the ''inner'' circle), an <math>O</math> signal going counter-clockwise, and an <math>S</math> switching betw ...>A</math>, the difference between the number of <math>I</math>'s and <math>O</math>'s must be a multiple of <math>5</math>.
  11 KB (1,934 words) - 12:18, 29 March 2024
• Basic Programming With Python
  ...ngs, tuples, but not lists!) Just like dictionaries, lookups for items are O(1) and insertions are as well!
  33 KB (5,277 words) - 22:14, 3 June 2023
• 1956 AHSME Problems/Problem 49
  Triangle <math>PAB</math> is formed by three tangents to circle <math>O</math> and <math>\angle APB = 40^{\circ}</math>; then <math>\angle AOB</mat .../math> bisects <math>\angle BAT</math> (to see this, draw radii from <math>O</math> to <math>AB</math> and <math>AT,</math> creating two congruent right
  1 KB (217 words) - 01:32, 3 January 2024
• 2018 AIME II Problems/Problem 14
  ...<math>ZW,CP,BQ</math> and <math>XY</math> are concurrent at a point <math>O</math>. Let <math>PQ \cap BC = M</math>. Then by La Hire's <math>A</math> l <cmath> -1 = (A,O;Y,X) \stackrel{M}{=} (A,Z;P,B) \stackrel{M}{=} (A,W;Q,C).</cmath>Therefore,
  9 KB (1,518 words) - 14:32, 28 January 2024
• UAB Math-by-Mail
  c/o Dr Alexander Blokh
  2 KB (388 words) - 18:15, 24 August 2020
• CyberMath Academy
  * Dr. Johanna O'Day – Researcher at Stanford Bio-X Interdisciplinary Biosciences Institut
  6 KB (788 words) - 19:10, 22 December 2022
• 2018 USAJMO Problems/Problem 3
  label("$O$", (0.03388760411534265,0.08889671794036069), NE * 0.5);
  8 KB (920 words) - 20:30, 4 November 2020

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