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• 2005 Indonesia MO Problems/Problem 7
  ...mark points <math>Y = (2b_1,b_2)</math>, <math>K = (x,y)</math>, and <math>Z = (x,b_2)</math>. {{Indonesia MO box|year=2005|num-b=6|num-a=8}}
  5 KB (959 words) - 20:57, 12 October 2019
• 2006 Indonesia MO Problems/Problem 7
  ...bc,ca</math> are rational numbers. Prove that there are integers <math>x,y,z</math>, not all of them are <math>0</math>, such that <math>ax+by+cz=0</mat ...math>(x,0,0)</math>. This solution set works because not all of <math>x,y,z</math> are equal to zero.
  2 KB (353 words) - 19:32, 16 October 2019
• 2007 Indonesia MO Problems
  [[2007 Indonesia MO Problems/Problem 1|Solution]] [[2007 Indonesia MO Problems/Problem 2|Solution]]
  4 KB (619 words) - 17:18, 12 February 2020
• 2000 Pan African MO Problems/Problem 4
  <cmath> z^2=x^2+y^2 </cmath> <cmath> (z+c)^2=(x+a)^2+(y+b)^2 </cmath>
  2 KB (273 words) - 13:34, 17 December 2019
• 2000 Pan African MO Problems/Problem 1
  ...o the equation are <math>\boxed{x = \frac{3 \pi}{4} + \pi n, n \in \mathbb{Z}}</math>. {{Pan African MO box
  2 KB (305 words) - 06:07, 23 February 2023
• 2000 Pan African MO Problems
  [[2000 Pan African MO Problems/Problem 1|Solution]] [[2000 Pan African MO Problems/Problem 2|Solution]]
  2 KB (393 words) - 13:39, 4 December 2019
• 2007 Indonesia MO Problems/Problem 6
  Find all triples <math> (x,y,z)</math> of real numbers which satisfy the simultaneous equations <cmath>y = z^3 + z - 8</cmath>
  2 KB (340 words) - 01:16, 19 March 2020
• 2022 AIME I Problems/Problem 15
  Let <math>x,</math> <math>y,</math> and <math>z</math> be positive real numbers satisfying the system of equations: Then <math>\left[ (1-x)(1-y)(1-z) \right]^2</math> can be written as <math>\frac{m}{n},</math> where <math>m
  15 KB (2,208 words) - 01:25, 1 February 2024
• 2004 Pan African MO Problems/Problem 6
  ...the [[circumcircle]] of <math>XYZ</math> for any three points <math>X, Y, Z</math>, and use <math>\Omega</math> to represent the circumcircle of <math> {{Pan African MO box|year=2004|num-b=5|after=Last Problem}}
  3 KB (572 words) - 13:48, 27 May 2024
• 2021 Fall AMC 12B Problems/Problem 22
  .../math> be the point such that <math>ABCD</math> is a rectangle. Then <math>MO\perp AB</math> and <math>MP\perp AB</math>. Let <math>\theta = \angle BAC</ <cmath>OP=MP-MO=AM\cot\theta - BM\tan\theta = 5(\tfrac 43 - \tfrac 34) = \boxed{\textbf{(C)
  6 KB (943 words) - 00:41, 6 August 2023
• 2023 AIME I Problems/Problem 8
  ...{AB},</math> and <math>\overline{BC}</math> at <math>X,Y,</math> and <math>Z,</math> respectively. Moreover, suppose that <math>R,S,</math> and <math>T< pair A, B, C, D, O, P, R, S, T, X, Y, Z, Q;
  17 KB (2,612 words) - 14:54, 3 July 2023
• 2018 TSTST Problems
  ...to {\mathbb Z}</math> such that for any polynomials <math>p,q \in {\mathbb Z}[x]</math>, ...iangle BIC</math> and <math>\triangle BAD</math>, respectively. Line <math>MO</math> meets <math>\omega</math> at <math>X</math> and <math>Y</math>, whil
  5 KB (930 words) - 08:38, 22 February 2023
• 2023 AMC 12B Problems/Problem 25
  Since <math>A</math> is folded onto <math>O</math>, <math>AM = MO</math> where <math>M</math> is the intersection of <math>AO</math> and the Let the inner pentagon be <math>Z</math>.
  19 KB (2,971 words) - 00:31, 4 June 2024
• Sharygin Olympiads, the best
  ...math> the midpoint <math>AB, D</math> the point on the line <math>CO, DO = MO, \alpha = \angle CBM, b = OM.</math> Denote <math>\Omega = \odot ABC, Z = BB' \cap AA', D = AQ \cap BP.</math>
  29 KB (4,997 words) - 18:06, 16 May 2024
• Arcticturn Prep
  ...are real numbers <math>a</math> and <math>b</math> such that <math>x + y + z = a + bi</math>. Find <math>a^2 + b^2</math>. ...math>z</math> with the properties that <math>|z|=1</math> and <math>z^{6!}-z^{5!}</math> is a real number. Find the remainder when <math>N</math> is div
  12 KB (2,039 words) - 20:01, 24 June 2024

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