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• LaTeX:Symbols
  |<math>\bot</math>||\bot||<math>\vdash</math>||\vdash||<math>\dashv</math>||\dashv :<tt>(\frac{a}{x} )^2</tt>
  16 KB (2,324 words) - 16:50, 19 February 2024
• Mock AIME 3 Pre 2005 Problems/Problem 14
  ...ath>QP</math>. Thus, <math>O_3R \bot PQ</math> and <math>|PR|=\frac{|PQ|}{2}=16</math> Then, <math>A_1=\frac{|AD| \times h_1}{2}</math>, thus <math>h_1=\frac{2}{3}A_1</math>
  3 KB (563 words) - 02:05, 25 November 2023
• 1965 IMO Problems/Problem 5
  Point <math>Q = OB \cap MQ</math>, <math>MQ \bot OB</math>. Solving: <math>x_{Q}=\frac{1}{b^{2}+c^{2}}\left[b^{2}\lambda+\frac{c^{2}(\lambda-a)b}{b-a}\right]</math>.
  1 KB (269 words) - 00:23, 9 December 2022
• 2002 AMC 12A Problems/Problem 23
  M = (B + C)/2; ...(with sides <math>12,7,9</math>), we have <math>[\triangle ABD]= \sqrt{14(2)(7)(5)} = 14\sqrt5 \Longrightarrow \boxed{\text{D}}</math>.
  6 KB (899 words) - 01:41, 5 July 2023
• 2012 IMO Problems/Problem 1
  ...l <math>AGLJ</math> is cyclic because <math>\angle JAL = \frac{\angle BAC}{2} = \angle YGM = \angle YGL = \angle JGL</math>. Again, <math>\triangle AJL ==Solution 2==
  7 KB (1,189 words) - 01:22, 19 November 2023
• 2011 AIME II Problems/Problem 10
  ...e between the [[midpoint]]s of the two chords is 12. The quantity <math>OP^2</math> can be represented as <math>\frac{m}{n}</math>, where <math>m</math> ..., <math>OE = \sqrt{25^2 - 15^2} = 20</math>, and <math>OF = \sqrt{25^2 - 7^2} = 24</math>.
  11 KB (1,720 words) - 03:12, 18 December 2023
• 1967 AHSME Problems
  <math> \text{(A)}\ 2\qquad\text{(B)}\ 4\qquad\text{(C)}\ 6\qquad\text{(D)}\ 8\qquad\text{(E)}\ 9 ==Problem 2==
  20 KB (3,108 words) - 14:14, 20 February 2020
• 2013 AIME II Problems/Problem 10
  The equation for Circle O is <math>x^2+y^2=13</math>, and let the slope of the line<math>AKL</math> be <math>k</math>, Then we get <math>(k^2+1)x^2-2k^2(4+\sqrt{13})x+k^2\cdot (4+\sqrt{13})^2-13=0</math>. According to [[Vieta's Formulas]], we get
  5 KB (823 words) - 17:57, 29 December 2023
• 1967 AHSME Problems/Problem 33
  ...ne{CB}</math>, so that they are mutually tangent. If <math>\overline{CD} \bot \overline{AB}</math>, then the ratio of the shaded area to the area of a ci <math>\textbf{(A)}\ 1:2\qquad
  2 KB (232 words) - 01:40, 16 August 2023
• 2007 IMO Problems/Problem 4
  real c=8.1,a=5*(c+sqrt(c^2-64))/6,b=5*(c-sqrt(c^2-64))/6; pair A=(0,0),B=(c,0),R=(c/2,-sqrt(25-(c/2)^2));
  8 KB (1,480 words) - 14:52, 5 August 2022
• 2019 AIME I Problems/Problem 15
  ...hat <math>AP=5</math>, <math>PB=3</math>, <math>XY=11</math>, and <math>PQ^2 = \frac{m}{n}</math>, where <math>m</math> and <math>n</math> are relativel O1=extension((A+P)/2, (A+P)/2+(0, 1), A, O);
  13 KB (2,252 words) - 11:32, 1 February 2024
• Mathcounts Week/Countdown Round
  ...son DeleteSticky was disqualified, although it is likely DeleteSticky is a bot or a glitch in the system. 2 aaravdodhia
  11 KB (1,044 words) - 17:36, 11 January 2021
• 2020 USOJMO Problems/Problem 4
  ==Solution 2== ...math>y+x+\angle GBE=\frac{\pi}{2}</math>, or <math>\angle GBE = \frac{\pi}{2}-x-y</math>.
  6 KB (1,131 words) - 19:15, 6 October 2023
• 2021 AIME II Problems/Problem 14
  ...angle BCA, </math> and <math>\angle XOY</math> are in the ratio <math>13 : 2 : 17, </math> the degree measure of <math>\angle BAC</math> can be written &= 2\angle BCA + \frac12\angle BOC \hspace{10mm} &&\text{by Inscribed Angle Theo
  10 KB (1,526 words) - 16:50, 25 December 2022
• 2024 AIME II Problems/Problem 8
  ...,0.1)..(-0.8,-0.03)..(-0.4,-0.11)..(0,-0.15)..(0.4,-0.11)..(0.8,-0.03)..(1.2,0.1)); draw((0,2.4)--(0,-0.15));
  5 KB (880 words) - 16:18, 23 April 2024
• 2024 AIME II Problems/Problem 10
  real c=8.1,a=5*(c+sqrt(c^2-64))/6,b=5*(c-sqrt(c^2-64))/6; pair B=(0,0),C=(c,0), D = (c/2-0.01, -2.26);
  17 KB (2,854 words) - 15:18, 23 April 2024