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• 2007 AMC 10A Problems/Problem 24
  ...and <math>B</math> each have radius <math>2</math>, as shown. Point <math>O</math> is the [[midpoint]] of <math>\overline{AB}</math>, and <math>OA = 2\ label("$O$",(0,0),dir(270));
  3 KB (439 words) - 15:39, 3 June 2021
• 1998 AHSME Problems/Problem 26
  label("\(O\)",circumcenter(A,B,C),SW);
  3 KB (391 words) - 14:30, 5 July 2013
• 1995 USAMO Problems
  Given a nonisosceles, nonright triangle <math>\, ABC, \,</math> let <math>\, O \,</math> denote the center of its circumscribed circle, and let <math>\, A
  3 KB (540 words) - 13:31, 4 July 2013
• 2004 AMC 12B Problems/Problem 19
  pair P=(D+G)/2, Q=(D+H)/2, R=(B+E)/2, T=(A+H)/2, O=(E+G)/2; dot(E);dot(F);dot(G);dot(H);dot(O);
  3 KB (520 words) - 19:12, 20 November 2023
• 2007 AMC 10B Problems/Problem 11
  Let <math>\triangle ABC</math> have vertex <math>A</math> and center <math>O</math>, with foot of altitude from <math>A</math> intersecting <math>BC</ma pair O=circumcenter(A,B,C);
  5 KB (851 words) - 22:02, 26 July 2021
• Isogonal conjugate
  ...nt <math>O</math> be called isogonals with respect to the pair <math>(\ell,O).</math> ...h the line <math>\ell</math> and the origin coincides with the point <math>O,</math> then the isogonals define the equations <math>y = \pm kx,</math> an
  54 KB (9,416 words) - 08:40, 18 April 2024
• 2008 AMC 10A Problems
  Points <math>A</math> and <math>B</math> lie on a circle centered at <math>O</math>, and <math>\angle AOB = 60^\circ</math>. A second circle is internal
  14 KB (2,138 words) - 15:08, 18 February 2023
• 2008 AMC 12A Problems
  Points <math>A</math> and <math>B</math> lie on a circle centered at <math>O</math>, and <math>\angle AOB = 60^\circ</math>. A second circle is internal ...math>y</math> axis, and one on the positive <math>z</math> axis. Let <math>O</math> be the origin. What is the volume of <math>OABC</math>?
  13 KB (2,025 words) - 13:56, 2 February 2021
• 2008 AMC 12A Problems/Problem 13
  ...ts <math>A</math> and <math>B</math> lie on a [[circle]] centered at <math>O</math>, and <math>\angle AOB = 60^\circ</math>. A second circle is internal pair O=(0,0), A=(3,0), B=(3/2,3/2*3^.5), C=(3^.5,1), D=(3^.5,0), F=(1.5*3^.5,1.5),
  4 KB (630 words) - 20:32, 4 June 2021
• 2008 AMC 12A Problems/Problem 18
  ...math>y</math>-axis, and one on the positive <math>z</math>-axis. Let <math>O</math> be the [[origin]]. What is the volume of [[tetrahedron]] <math>OABC< ..."A",(8,0),(1,0));label("B",(0,10),(0,1));label("C",(-3,-4),(-1,-1));label("O",(0,0),(1,1));
  2 KB (302 words) - 04:51, 16 January 2023
• 2008 AMC 12A Problems/Problem 20
  pair O=incenter(A,C,D), P=incenter(B,C,D); dot(O);dot(P);
  6 KB (951 words) - 16:31, 2 August 2019
• 2008 AMC 12A Problems/Problem 22
  Let one of the mats be <math>ABCD</math>, and the center be <math>O</math> as shown: label("\(O\)",(0.00,-0.10),E);
  10 KB (1,518 words) - 17:00, 16 May 2023
• 2008 AMC 10B Problems
  ...th>OA</math> is rotated <math>90^\circ</math> counterclockwise about <math>O</math>. What are the coordinates of the image of <math>A</math>?
  12 KB (1,838 words) - 16:52, 7 October 2022
• 2008 AMC 12B Problems
  On circle <math>O</math>, points <math>C</math> and <math>D</math> are on the same side of di pair O = (0,0);
  14 KB (2,199 words) - 13:43, 28 August 2020
• 2008 AMC 12B Problems/Problem 4
  On circle <math>O</math>, points <math>C</math> and <math>D</math> are on the same side of di pair O = (0,0);
  1 KB (183 words) - 22:35, 10 June 2017
• 2008 AMC 12B Problems/Problem 9
  ...erline{AB}</math>, and <math>O</math> the center of the circle. Then <math>O</math>, <math>C</math>, and <math>D</math> are collinear, and since <math>D pair O = (0,0), A=(5,0), B = IP(p,CR(A,6)), C = IP(p,CR(A,3)), D=IP(A--B,O--C);
  2 KB (319 words) - 13:48, 15 February 2021
• 2008 AIME I Problems/Problem 14
  pair O = (0,0), B = O - (9,0), A= O + (9,0), C=A+(18,0), T = 9 * expi(-1.2309594), P = foot(A,C,T); draw(Circle(O,9)); draw(B--C--T--O); draw(A--P); dot(A); dot(B); dot(C); dot(O); dot(T); dot(P);
  8 KB (1,333 words) - 00:18, 1 February 2024
• Mock AIME 5 Pre 2005 Problems
  ...and such that <math>\frac {j + k}{j - k} = \frac {o}{p}</math>, find <math>o + p.</math>
  6 KB (909 words) - 07:27, 12 October 2022
• Mock AIME 1 2007-2008 Problems/Problem 14
  ...math>AB = BC</math>. Let <math>D</math> be the intersection of <math>\odot O</math> and <math>OC</math> such that <math>CD = \frac {1}{18}</math> and <m pair O = (0,0), A=(r,0), B= A*dir(112.02432), C=2*B-A;
  2 KB (375 words) - 15:23, 25 November 2009
• Mock AIME 1 2007-2008 Problems
  ...math>AB = BC</math>. Let <math>D</math> be the intersection of <math>\odot O</math> and <math>OC</math> such that <math>CD = \frac {1}{18}</math> and <m
  6 KB (992 words) - 14:15, 13 February 2018

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