Create the page "O o o-o o o" on this wiki! See also the search results found.

• 2015 UMO Problems
  A triangular pyramid with apex <math>O</math> and base <math>\triangle{ABC}</math> has the property that the perim ...the minimum possible height from <math>\triangle{ABC}</math> to apex <math>O</math>? Show that this height is achievable.
  3 KB (423 words) - 02:51, 6 November 2015
• 2015 UMO Problems/Problem 6
  A triangular pyramid with apex <math>O</math> and base <math>\triangle{ABC}</math> has the property that the perim ...the minimum possible height from <math>\triangle{ABC}</math> to apex <math>O</math>? Show that this height is achievable.
  642 bytes (99 words) - 03:03, 6 November 2015
• 2015 AMC 8 Problems/Problem 2
  Point <math>O</math> is the center of the regular octagon <math>ABCDEFGH</math>, and <mat pair A,B,C,D,E,F,G,H,O,X;
  5 KB (801 words) - 10:55, 14 January 2024
• 2015 AMC 8 Problems/Problem 11
  ...bile license plates have four symbols. The first must be a vowel (A, E, I, O, or U), the second and third must be two different letters among the 21 non
  2 KB (319 words) - 23:58, 16 May 2023
• 2015 AMC 8 Problems
  Point <math>O</math> is the center of the regular octagon <math>ABCDEFGH</math>, and <mat pair A,B,C,D,E,F,G,H,O,X;
  16 KB (2,322 words) - 14:04, 2 February 2024
• 2019 AMC 12A Problems
  ...of its sides is tangent to the sphere. What is the distance between <math>O</math> and the plane determined by the triangle? Circles <math>\omega</math> and <math>\gamma</math>, both centered at <math>O</math>, have radii <math>20</math> and <math>17</math>, respectively. Equil
  14 KB (2,180 words) - 06:56, 9 June 2024
• 2016 AMC 10B Problems
  ...h> centered at <math>A’(5,6)</math>. What distance does the origin <math>O(0,0)</math>, move under this transformation?
  12 KB (1,868 words) - 17:50, 30 December 2023
• 2016 AMC 10B Problems/Problem 20
  ...h> centered at <math>A’(5,6)</math>. What distance does the origin <math>O(0,0)</math>, move under this transformation? pair O = (3.,0.), A = (2.,2.), B = (2.,1.), C = (4.203155585,5.592712848525), D =
  8 KB (1,011 words) - 11:57, 28 February 2024
• 2016 AIME I Problems/Problem 6
  ...sult in <math>LI</math> being greater than <math>DL</math>) and that <math>O</math> and <math>I</math> are collinear. Next, if <math>OI=d</math>, <math>
  14 KB (2,397 words) - 20:04, 27 August 2023
• Commonly Used Language on AoPS
  ...ng a major forum. It is meant to look like a person bowing down, with the "o" being the head, the "r" being the arms and torso, and the "z" being the le
  2 KB (292 words) - 16:51, 13 March 2024
• 2016 AIME II Problems/Problem 14
  ...dihedral angle (the angle between the two planes). There is a point <math>O</math> whose distance from each of <math>A,B,C,P,</math> and <math>Q</math> ...h>P, Q, O</math> are collinear, and <math>OP=OQ</math>, we must have <math>O</math> is the midpoint of <math>PQ</math>. Now, Let <math>K</math> be the
  15 KB (2,560 words) - 01:44, 1 July 2023
• 2016 AIME II Problems/Problem 9
  ...000 \implies b^4 -2b^2 -1 = 1000-200 \implies b^4 - 2b^2 = 801 \implies \O.</cmath> ...0-3\cdot 2^{k-3} \implies 2^k +450k -3k\cdot 2^{k-3} + 1 = 1000 \implies \O.</cmath>
  6 KB (983 words) - 01:18, 2 February 2023
• 2016 AIME II Problems
  ...dihedral angle (the angle between the two planes). There is a point <math>O</math> whose distance from each of <math>A,B,C,P,</math> and <math>Q</math>
  8 KB (1,312 words) - 21:16, 3 March 2021
• 1964 AHSME Problems/Problem 17
  ...ts are drawn connecting these points to each other and to the origin <math>O</math>. ...<math>R</math>, and that fourth point will form a parallelogram with <math>O, P, Q</math>.
  2 KB (305 words) - 15:10, 5 July 2021
• 2006 iTest Problems
  The point <math>P</math> is a point on a circle with center <math>O</math>. Perpendicular lines are drawn from <math>P</math> to perpend \text{(O) }\text{none of the above}\qquad</math>
  31 KB (4,811 words) - 00:02, 4 November 2023
• 1954 AHSME Problems/Problem 37
  label("$O$",pI+(-0.2,0.166),f);
  3 KB (560 words) - 10:11, 3 May 2020
• 1982 AHSME Problems/Problem 18
  triple A=(0,0,r), B=(0,r,r), C=(1,r,r), D=(1,0,r), E=O, F=(0,r,0), G=(1,0,0), H=(1,r,0);
  2 KB (294 words) - 08:42, 15 April 2016
• 2016 USAMO Problems
  ...ABC</math> be an acute triangle, and let <math>I_B, I_C,</math> and <math>O</math> denote its <math>B</math>-excenter, <math>C</math>-excenter, and cir ...t <math>\overline{OI}</math> is parallel to <math>\ell,</math> where <math>O</math> is the circumcenter of triangle <math>ABC,</math> and <math>I</math>
  4 KB (608 words) - 13:49, 22 November 2023
• 2016 USAJMO Problems
  Let <math>\triangle ABC</math> be an acute triangle, with <math>O</math> as its circumcenter. Point <math>H</math> is the foot of the perpend Given that <cmath>AH^2=2\cdot AO^2,</cmath>prove that the points <math>O,P,</math> and <math>Q</math> are collinear.
  3 KB (414 words) - 16:43, 5 August 2023
• 2016 USAJMO Problems/Problem 5
  Let <math>\triangle ABC</math> be an acute triangle, with <math>O</math> as its circumcenter. Point <math>H</math> is the foot of the perpend Given that <cmath>AH^2=2\cdot AO^2,</cmath>prove that the points <math>O,P,</math> and <math>Q</math> are collinear.
  10 KB (1,733 words) - 19:15, 14 June 2020

View (previous 20 | next 20) (20 | 50 | 100 | 250 | 500)