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• 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
• 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
• 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
• 1959 AHSME Problems
  Each edge of a cube is increased by <math>50</math>%. The percent of increase of the surfa <math>\textbf{(A)}\ 50 \qquad\textbf{(B)}\ 125\qquad\textbf{(C)}\ 150\qquad\textbf{(D)}\ 300
  22 KB (3,345 words) - 20:12, 15 February 2023
• Construction
  ...to mark off segments, draw circles and arcs, and draw straight lines) are a branch of [[geometry]] that rely on the use of basic geometrical [[axiom]]s A '''compass''' is a tool that can draw circles and arcs of circles.
  3 KB (443 words) - 20:52, 28 August 2014
• Isogonal conjugate
  ...nal conjugates''' are pairs of [[point]]s in the [[plane]] with respect to a certain [[triangle]]. ...ll</math> and a point <math>O</math> lying on <math>\ell</math> be given. A pair of lines symmetric with respect to <math>\ell</math> and containing t
  54 KB (9,416 words) - 08:40, 18 April 2024
• Shoelace Theorem
  The '''Shoelace Theorem''' is a nifty formula for finding the [[area]] of a simple [[polygon]] given the [[Cartesian coordinate system|coordinates]] of ...math>, listed in clockwise order. Then the area (<math>A</math>) of <math>P</math> is
  8 KB (1,358 words) - 15:32, 22 February 2024
• 2008 USAMO Problems/Problem 3
  (''Gabriel Carroll'') Let <math>n</math> be a positive integer. Denote by <math>S_n</math> the set of points <math>(x, y) ...math> appears in exactly one of the <math>m</math> paths in <math>\mathcal{P}</math>).
  9 KB (1,585 words) - 01:00, 14 August 2014
• Millennium Problems
  ...set of seven problems for which the [[Clay Mathematics Institute]] offered a US \$7 million prize fund (\$1 million per problem) to celebrate the new mi ...Conjecture]], the [[Hodge Conjecture]], the [[Navier-Stokes Equations]], [[P versus NP]], the [[Poincaré Conjecture]], the [[Riemann Hypothesis]], and
  13 KB (1,969 words) - 17:57, 22 February 2024
• 1995 IMO Problems/Problem 1
  ...h>XY</math> meets <math>BC</math> at <math>Z</math>. Let <math>P</math> be a point on the line <math>XY</math> other than <math>Z</math>. The line <math Think about Radical Axis, Power of a Point and Radical Center.
  5 KB (847 words) - 19:03, 12 October 2021
• 2008 iTest Problems
  ...s as a Renewable Energy Engineer for the Southern Company, and Hannah runs a lab at Jupiter Falls University where she researches biomass (renewable fue When the Kubiks went on vacation to San Diego last year, they spent a day at the San Diego Zoo.
  71 KB (11,749 words) - 01:31, 2 November 2023
• 2005 AMC 8 Problems
  Connie multiplies a number by 2 and gets 60 as her answer. However, she should <math> \textbf{(A)}\ 7.5\qquad\textbf{(B)}\ 15\qquad\textbf{(C)}\ 30\qquad\textbf{(D)}\ 120\q
  13 KB (1,821 words) - 22:18, 5 December 2023
• 2001 USAMO Problems/Problem 6
  Each point in the plane is assigned a real number such that, for any triangle, the number at the center of its in '''Lemma''': If <math>ABCD</math> is an isosceles trapezoid, then <math>a + c = b + d</math>.
  2 KB (302 words) - 18:11, 22 February 2016
• 1992 USAMO Problems/Problem 4
  ...phere through <math>A'</math>, <math>B'</math>, <math>C'</math>, and <math>P</math>. Prove that <math>AA'=BB'=CC'</math>. ...he base angles are equal. Thus, <math>AP=BP</math>. Similarly, <math>A'P=B'P</math>. Thus, <math>AA'=BB'</math>. By symmetry, <math>BB'=CC'</math> and <
  5 KB (807 words) - 18:37, 25 June 2021
• 1974 USAMO Problems/Problem 4
  A father, mother and son hold a family tournament, playing a two person board game with no ties. The tournament rules are: 3) Play the first game against the stronger of the other two players (the so
  6 KB (1,037 words) - 23:42, 11 May 2018
• 2004 AMC 10B Problems/Problem 4
  ...at are visible. What is the largest number that is certain to divide <math>P</math>? <math> \mathrm{(A) \ } 6 \qquad \mathrm{(B) \ } 12 \qquad \mathrm{(C) \ } 24 \qquad \mathrm{(
  2 KB (348 words) - 23:42, 16 January 2024
• 2009 AMC 10B Problems/Problem 22
  ...pieces as shown in this top view, where <math>M</math> is the midpoint of a top edge. The piece whose top is triangle <math>B</math> contains <math>c</ pair P=foot((1,-1),(1,1),(-1,0));
  12 KB (1,868 words) - 03:36, 30 September 2023
• 2009 AIME I Problems
  ...s <math>3</math> distinct digits which, when read from left to right, form a geometric sequence. Find the difference between the largest and smallest g ...s a complex number <math>z</math> with imaginary part <math>164</math> and a positive integer <math>n</math> such that
  7 KB (1,152 words) - 02:24, 23 July 2021
• 2009 AIME I Problems/Problem 5
  ...erline{CL}</math> is the angle bisector of angle <math>C</math>. Let <math>P</math> be the point of intersection of <math>\overline{BK}</math> and <math pair A=(0,0), B=(30*sqrt(331),0), C, K, L, M, P;
  8 KB (1,224 words) - 19:52, 7 March 2024

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