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• 1997 PMWC Problems/Problem I6
  ...>6</math> small ones and had <math>\textdollar 5</math> left. How much was a small exercise book? <math>l=10</math>
  660 bytes (105 words) - 14:23, 20 April 2014
• 1997 PMWC Problems/Problem I11
  A rectangle <math>ABCD</math> is made up of five small congruent rectangles a pair A=(0,0),B=(0,-2.5),C=(3,-2.5),D=(3,0);
  944 bytes (154 words) - 12:44, 13 August 2014
• 1961 IMO Problems
  \quad x + y + z \!\!\! &= a \; \, \\ ...</math> and <math>b </math> are constants. Give the conditions that <math>a </math> and <math>b </math> must satisfy so that <math>x, y, z </math> (the
  3 KB (425 words) - 21:18, 20 August 2020
• 1961 IMO Problems/Problem 6
  ...o not form a triangle.) What is the locus of point <math>G</math> as <math>A', B', C'</math> range independently over the plane <math>\epsilon</math>? ...\prime B^\prime C^\prime</math>. It is obvious that the centroid of <math>A^\prime B^\prime C^\prime</math> can be any point on plane <math>\epsilon</m
  2 KB (301 words) - 23:29, 18 July 2016
• 1999 USAMO Problems/Problem 5
  ...ut producing SOS then the game is a draw. Prove that the second player has a winning strategy. ...n S in <math>l + 3</math> and if <math>l < m</math> he fills an S in <math>l-3</math>.
  2 KB (433 words) - 13:35, 4 July 2013
• 2006 Cyprus MO/Lyceum/Problem 12
  <math>\mathrm{(A)}\ 8\qquad\mathrm{(B)}\ 0\qquad\mathrm{(C)}\ 11\qquad\mathrm{(D)}\ 5\qquad\ {{CYMO box|year=2006|l=Lyceum|num-b=11|num-a=13}}
  701 bytes (92 words) - 16:51, 23 November 2016
• 2006 Cyprus MO/Lyceum/Problem 17
  ...Gamma</math> is equilateral triangle of side <math>\alpha</math> and <math>A\Delta=BE=\frac{\alpha}{3}</math>. The measure of the angle <math>\angle\Gam <math>\mathrm{(A)}\ 60^\circ\qquad\mathrm{(B)}\ 50^\circ\qquad\mathrm{(C)}\ 40^\circ\qquad\m
  789 bytes (123 words) - 22:00, 30 November 2015
• 2006 Cyprus MO/Lyceum/Problem 19
  ...[isosceles triangle]] with<math> AB=A\Gamma=\sqrt2</math> and <math>\angle A=45^\circ</math>. If <math>B\Delta</math> is an [[altitude]] of the [[triang <math>\mathrm{(A)}\ \frac{4\sqrt3-\pi}{6}\qquad\mathrm{(B)}\ 4\left(\sqrt2-\frac{\pi}{3}\rig
  1 KB (214 words) - 23:44, 22 December 2016
• 2006 Cyprus MO/Lyceum/Problem 29
  {{CYMO box|year=2006|l=Lyceum|num-b=28|num-a=30}}
  99 bytes (12 words) - 23:19, 19 December 2019
• 1960 IMO Problems/Problem 6
  ...ne of revolution with an inscribed sphere tangent to the base of the cone. A cylinder is circumscribed about this sphere so that one of its bases lies i a) Prove that <math>V_1 \neq V_2</math>;
  7 KB (1,214 words) - 18:49, 29 January 2018
• Asymptote: Useful functions
  The bundled <code>markers</code> package provides a useful function for marking angles. The exact same function exists in the < Label ''L''="", int ''n''=1, real ''radius''=0, real ''space''=0,<br/>
  4 KB (646 words) - 21:18, 26 March 2024
• Asymptote: CSE5
  ...of two paths without common points, which may be useful if you try to draw a picture just from its verbal description and do not want to make any calcul CSE5 contains doubles of each function; a function with a full name and a function with an abbreviated name.
  4 KB (607 words) - 15:09, 30 June 2020
• Excircle
  ...is a [[circle]] [[Tangent line|tangent]] to the extensions of two sides of a [[triangle]] and the third side. pair excenter(pair A, pair B, pair C){
  5 KB (843 words) - 03:02, 1 July 2020
• 2001 USAMO Problems/Problem 2
  ...t <math>AD_2</math> at two points, the closer of which to the vertex <math>A</math> is denoted by <math>Q</math>. Prove that <math>AQ = D_2P</math>. It is well known that the excircle opposite <math>A</math> is tangent to <math>\overline{BC}</math> at the point <math>D_2</mat
  11 KB (2,091 words) - 08:35, 16 November 2017
• L'Hôpital's Rule
  '''L'Hopital's Rule''' is a theorem dealing with [[limit]]s that is very important to [[calculus]]. The definition of a derivative is <math>f'(x) = \lim_{h\rightarrow 0} \frac{f(x+h)-f(x)}{h}</ma
  2 KB (475 words) - 15:04, 24 March 2022
• Squeeze Theorem
  ...so called the '''Sandwich Theorem''' or the '''Squeeze Play Theorem''') is a relatively simple [[theorem]] that deals with [[calculus]], specifically [[ ...as <math>x</math> approaches <math>S</math>, then <math>\lim_{x\to S}f(x)=L</math>.
  2 KB (439 words) - 15:36, 1 December 2015
• De Longchamps point
  label("L",(34,50),(1,1)); </asy>|right|The de Longchamps <br />point (<math>L</math>) is the the <br />[[orthocenter]] (<math>H</math>) reflected <br />
  10 KB (1,780 words) - 09:23, 17 November 2022
• Graph (graph theory)
  ...[[empty set | nonempty]] [[set]] of [[vertex|vertices]] that are joined by a number (possibly zero) of [[edge]]s. Graphs are frequently represented gra ...' graphs: there is at most one edge joining two vertices, no edge may join a vertex to itself, and the edges are not directed. For graphs with multiple
  8 KB (1,428 words) - 10:26, 27 August 2020
• 2007 AMC 10A Problems
  {{AMC10 Problems|year=2007|ab=A}} ...ath>25\%</math> discount. Pam buys 5 tickets using a coupon that gives her a <math>30\%</math> discount. How many more dollars does Pam pay than Susan?
  13 KB (2,058 words) - 17:54, 29 March 2024
• 2007 AMC 10A Problems/Problem 21
  ...n a [[cube]] that has a [[surface area]] of <math>24</math> square meters. A second cube is then inscribed within the sphere. What is the surface area i <math>\text{(A)}\ 3 \qquad \text{(B)}\ 6 \qquad \text{(C)}\ 8 \qquad \text{(D)}\ 9 \qquad
  4 KB (609 words) - 14:41, 3 December 2023

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