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• 2008 AIME II Problems/Problem 9
  ...>xy</math>-plane, <math>r</math> be the length <math>OP</math> where <math>O</math> is the origin, and <math>\theta</math> be the inclination of OP to t Since <math>R+R^{7}=O, R^2+R^6=O, R^3+R^5=O, I+R^4=O</math>, so we have <math>R^6\begin{pmatrix}5\\0\end{pmatrix}+(-R^6-R^7)\beg
  5 KB (725 words) - 22:37, 28 January 2024
• 2008 AIME II Problems/Problem 11
  Let the incenter be O and the altitude from A to <math>\overline{BC}</math> be T. Note that by AA
  6 KB (1,065 words) - 20:12, 9 August 2022
• 2005 USAMO Problems/Problem 3
  path O=circumcircle(B1,C1,P); pair Q=IntersectionPoint(O,B--C,1);
  6 KB (1,117 words) - 01:17, 11 October 2021
• 2008 AMC 10B Problems/Problem 10
  Let the center of the circle be <math>O</math>, and let <math>D</math> be the intersection of <math>\overline{AB}</ 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);
  1 KB (247 words) - 12:36, 7 June 2021
• 2008 AMC 10B Problems/Problem 14
  ...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>? <!-- don't Rotate this triangle <math>90^\circ</math> counterclockwise around <math>O</math>, and you will find that <math>A</math> will end up in the second qua
  3 KB (444 words) - 04:45, 21 August 2023
• 2001 Iran NMO (Round 3) Problems/Problem 5
  path O=circumcircle(A,B,C); pair M=IntersectionPoint(A--Ia,O,1);
  3 KB (437 words) - 15:47, 27 April 2008
• 2008 USAMO Problems/Problem 2
  ...le OFA = 90^{\circ}</math>, as this would immediately prove that <math>A,P,O,F,N</math> are concyclic. ...and <math>OD</math> bisects exterior <math>\angle FDE</math>, making <math>O</math> the <math>F</math>-excentre of <math>\triangle FED</math>. This impl
  20 KB (3,565 words) - 11:54, 1 May 2024
• 1966 AHSME Problems/Problem 8
  Let <math>O</math> be the center of the circle of radius <math>10</math> and <math>P</m ...base <math>AB</math>. The height of <math>\triangle OAB</math> from <math>O</math> to <math>AB</math> is <math>\sqrt {\overline{OB}^2 - (\frac{\overlin
  2 KB (256 words) - 01:45, 26 June 2016
• 1995 AHSME Problems/Problem 26
  ...d <math>\overline{CD}</math> are diameters of the circle with center <math>O</math>, <math>\overline{AB} \perp \overline{CD}</math>, and chord <math>\ov pair O=origin, A=(-5,0), B=(5,0), C=(0,5), D=(0,-5), F=5*dir(40), E=intersectionpo
  2 KB (359 words) - 20:01, 23 January 2017
• 1995 AHSME Problems/Problem 18
  Two rays with common endpoint <math>O</math> forms a <math>30^\circ</math> angle. Point <math>A</math> lies on on Triangle <math>OAB</math> has the property that <math>\angle O=30^{\circ}</math> and <math>AB=1</math>.
  1 KB (167 words) - 13:59, 5 July 2013
• 1999 AHSME Problems/Problem 29
  pair O = (0,0), A = expi(pi/2), B = expi(7 * pi/6), C= expi(11 * pi / 6); D(CR(O, 1)); D(A--B--C--A); D(CR((0,-3/4),1/4));
  3 KB (522 words) - 11:39, 3 October 2023
• New York MathCounts
  * [[Home Educators Enrichment Group]] Coach Mary O'Keeffe.
  1 KB (138 words) - 09:58, 3 May 2010
• 1988 IMO Problems/Problem 1
  ...dii <math>R</math> and <math>r</math> (<math>R>r</math>) with center <math>O</math>. Fix <math>P</math> on the small circle and consider the variable c
  3 KB (545 words) - 11:32, 30 January 2021
• 2003 USAMO Problems/Problem 4
  pair B=origin, A=dir(theta), C=A+(rotate(78)*0.8*A), O=IP(CR(B,r),CR(A,r)); path c=CR(O,r);
  5 KB (820 words) - 02:39, 10 January 2023
• 2001 IMO Shortlist Problems/G2
  ...gle <math>ABC</math> issuing from the vertex <math>A</math>, and let <math>O</math> be the circumcenter of triangle <math>ABC</math>. Assume that <math>
  677 bytes (95 words) - 16:06, 17 March 2022
• Millennium Problems
  ...in polynomial time (as a function of the input, often expressed using big-O notation) can also be ''solved'' in polynomial time. The set <math>P</math> ...nt statement of the Riemann hypothesis is that <math>\pi(x)=\mathrm{Li}(x)+O(x^{1/2}\ln(x))</math>.
  13 KB (1,969 words) - 17:57, 22 February 2024
• Carnot's Theorem
  ...>O</math> to the sides (i.e., signed lengths of the pedal lines from <math>O</math>) is: pair a,b,c,O,i,d,f,g;
  4 KB (723 words) - 01:45, 18 February 2021
• 1995 IMO Problems/Problem 1
  ...<math>AC</math> is line <math>AM</math>. Also, the radical axis of <math>O</math> and the circle with diameter <math>BD</math> is line <math>DN</math>
  5 KB (847 words) - 19:03, 12 October 2021
• 2000 USAMO Problems/Problem 5
  Let the [[circumcenter]] of <math>\triangle ABC</math> be <math>O</math>, and let the center of <math>\omega_k</math> be <math>O_k</math>. <m <math>O</math> is the intersection of the perpendicular bisectors of <math>\overlin
  3 KB (609 words) - 09:52, 20 July 2016
• 2008 iTest Problems
  ...o hours it's left stuck to the wall. One morning, at around <math>9</math> o' clock, Tony sticks the spider to the wall in the living room three feet ab
  71 KB (11,749 words) - 01:31, 2 November 2023

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