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• Congruent (geometry)
  ...half-ray of the straight line <math>a'</math> emanating from a point <math>O'</math> of this line. Then in the plane <math>\alpha'</math> there is one a
  10 KB (1,655 words) - 21:43, 24 March 2022
• 2005 AMC 10A Problems/Problem 12
  pair O=(0,0), A=dir(0), B=dir(60), C=dir(120), D=dir(180); draw(D--E--B--O--C--B--A,linetype("4 4"));
  2 KB (246 words) - 16:40, 2 June 2024
• Circumcenter
  ...math> is equidistant from <math>A</math> and <math>{C}</math>; hence <math>O</math> also lies on the perpendicular bisector of <math>AC</math> (and is t
  2 KB (389 words) - 14:17, 4 August 2020
• Orthocenter
  ...C=(10,0), A1 = (B+C)/2, O = circumcenter(A,B,C), G = (A+B+C)/3, H = 3*G-2*O; draw(A1--G--O--cycle);
  5 KB (829 words) - 13:11, 20 February 2024
• Chord
  ...cle]] <math>O</math> is a [[line segment]] joining two [[point]]s on <math>O</math>. pair O=origin,A=dir(135),B=dir(30);
  522 bytes (103 words) - 12:16, 18 February 2018
• 2007 iTest Problems
  \text{(O) }2007\qquad</math> \text{(O) }520\qquad
  30 KB (4,794 words) - 23:00, 8 May 2024
• 1981 IMO Problems/Problem 5
  ...[[incenter]] and the [[circumcenter]] of the triangle and the point <math>O </math> are [[collinear]]. ...h>O</math> is clearly the circumcenter of <math>O_A O_B O_C </math>, <math>O</math> is collinear with the incenter and circumcenter of <math>ABC</math>,
  2 KB (373 words) - 23:09, 29 January 2021
• 2005 AMC 10A Problems
  Three tiles are marked <math>X</math> and two other tiles are marked <math>O</math>. The five tiles are randomly arranged in a row. What is the probabil pair O=(0,0), A=dir(0), B=dir(60), C=dir(120), D=dir(180);
  14 KB (2,026 words) - 11:45, 12 July 2021
• Euler line
  ...nter]] <math>H</math>, [[centroid]] <math>G</math>, [[circumcenter]] <math>O</math>, [[nine-point center]] <math>N</math> and [[De Longchamps point | de ...ntroid of <math>\triangle O_AO_BO_C</math>. Thus, <math>\mathcal{S}(\{O_A, O, G\}) = \{A, H, G\}</math>. As a homothety preserves angles, it follows tha
  59 KB (10,203 words) - 04:47, 30 August 2023
• Nine-point circle
  ...riangle AHZ.</math> Circumcenter of <math>\triangle ABC</math> point <math>O</math> is the midpoint <math>AZ,</math> point <math>D</math> is the midpoin Point <math>O</math> is the circumcenter of <math>\triangle XYZ \implies H</math> is the
  6 KB (994 words) - 16:02, 12 March 2024
• 1985 IMO Problems
  A circle with center <math>O</math> passes through the vertices <math>A</math> and <math>C</math> of the
  3 KB (465 words) - 03:00, 29 March 2021
• 1985 IMO Problems/Problem 1
  Let <math>O</math> be the center of the circle mentioned in the problem. Let <math>T</ Let <math>O </math> be the center of the circle mentioned in the problem, and let <math
  4 KB (684 words) - 07:28, 3 October 2021
• 2001 IMO Problems/Problem 1
  ...\triangle ABC</math> issuing from the vertex <math>A</math>, and let <math>O</math> be the [[circumcenter]] of triangle <math>\triangle ABC</math>. Assu Now <math>O</math> cannot coincide with <math>Y</math> (otherwise <math>\angle A</math>
  2 KB (417 words) - 17:24, 21 July 2018
• 2003 AMC 10A Problems/Problem 25
  ...since floor function always yields an integer, and 99 is divisible by 11 w/o any remainder). After we come to this conclusion, it becomes easy to solve
  6 KB (943 words) - 20:57, 29 May 2023
• 2004 AMC 10A Problems
  pair O=origin; fill(O--Arc(O, 2, 20, 160)--cycle, mediumgray);
  15 KB (2,092 words) - 20:32, 15 April 2024
• 2003 AMC 12A Problems/Problem 1
  Sum of first <math>n</math> odd numbers, is <math>S_O=n^{2}</math>, (O standing for odd). ...heir difference is <math>|1-0|=1</math>. Similarly, take take series <math>O</math> and <math>E_2</math>. The first terms are <math>1</math> and <math>2
  3 KB (436 words) - 20:31, 28 December 2021
• Sector
  pair O=origin, A=dir(angle2), B=dir(angle1); path sector=O--B--arc(O,1,angle1,angle2)--A--cycle;
  1 KB (178 words) - 21:12, 24 April 2008
• 2005 Alabama ARML TST Problems/Problem 3
  ...ngle and <math>COM</math> is a [[median of a triangle | median]], so <math>O</math> trisects <math>CO</math> and <math>R = CO = 2OM = 2r</math>.)
  1 KB (221 words) - 19:38, 6 February 2010
• 2020 AMC 10A Problems
  pair O = (0.851, 0.461); f[2] = E--F--G--O--N--cycle;
  13 KB (1,968 words) - 18:32, 29 February 2024
• Asymptote: Useful commands and their Output
  pair A,B,C,O,I; O=circumcenter(A,B,C); // olympiad - circumcenter
  6 KB (871 words) - 21:14, 12 June 2023

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