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• Pythagorean Theorem
  ...theorems in [[geometry]], and is one of the many tools in a good geometer's arsenal. A very large number of geometry problems can be solved by building ...let <math>ABC </math> be any right triangle with a right angle at <math>{} C </math>.
  5 KB (886 words) - 13:51, 15 May 2024
• Inequality
  ...slightly to [[number theory]]. They deal with [[relations]] of [[variable]]s denoted by four signs: <math>>,<,\ge,\le</math>. For two [[number]]s <math>a</math> and <math>b</math>:
  12 KB (1,806 words) - 06:07, 19 June 2024
• 1954 AHSME Problems/Problem 46
  In the diagram, if points <math>A, B</math> and <math>C</math> are points of tangency, then <math>x</math> equals: pair A=(-3*sqrt(3)/32,9/32), B=(3*sqrt(3)/32, 9/32), C=(0,9/16);
  3 KB (415 words) - 18:01, 24 May 2020
• 2015 IMO Problems
  We say that a finite set <math>\mathcal{S}</math> in the plane is <i> balanced </i> ...any two different points <math>A</math>, <math>B</math> in <math>\mathcal{S}</math>, there is
  4 KB (709 words) - 15:00, 1 June 2024
• Number theory/Advanced
  ...r theory include the [[Birch and Swinnerton-Dyer Conjecture]] and [[Fermat's Last Theorem]]. Denote by <math>\mathcal{H}</math> the upper half plane (those complex numbers with positive imaginary
  5 KB (849 words) - 16:14, 18 May 2021
• Circle
  A circle is defined as the [[set]] (or [[locus]]) of [[point]]s in a [[plane]] with an equal distance from a fixed point. The fixed point ...(h,k)</math>. Using the [[distance formula]], this gives <math>\sqrt{(x - h)^2 + (y - k)^2} = r</math> which is more commonly written as
  9 KB (1,581 words) - 18:59, 9 May 2024
• Ellipse
  Equivalently, it is defined as the [[locus]], or [[set]], of all [[point]]s <math>P</math> such that the sum of the distances from <math>P</math> to tw ...They occur in nature as well as in mathematics: as was proven in [[Kepler's Laws]], the planets all revolve about the sun in elliptical, not circular,
  5 KB (892 words) - 21:52, 1 May 2021
• Law of Cosines
  ...of Cosines''' is a theorem which relates the side-[[length]]s and [[angle]]s of a [[triangle]]. It can be derived in several different ways, the most co ...h> opposite [[angle]]s of measure <math>A</math>, <math>B</math> and <math>C</math>, respectively, the Law of Cosines states:
  6 KB (1,003 words) - 00:02, 20 May 2024
• Mock AMC
  * Look at famous theorems and formulas and see if there's any way you can make a good problem out of them. ! scope="row" | '''Mock AMC C'''
  51 KB (6,220 words) - 21:22, 17 July 2024
• Algebraic topology
  ...we can associate various algebraic objects, such as [[group]]s and [[ring]]s. ...ath> that start and end at <math>x</math>, i.e. all [[continuous function]]s <math>f:[0,1]\to X</math> with <math>f(0)=f(1)=x</math>. Call this collecti
  3 KB (479 words) - 15:35, 1 December 2015
• 2006 AIME I Problems/Problem 8
  ...as shown. Rhombuses <math> \mathcal{P, Q, R,} </math> and <math> \mathcal{S} </math> are [[congruent (geometry) | congruent]], and each has [[area]] <m ..., C=(5.85,-1.6), D=(4.2,-3.2), EE=(0,-3.2), F=(-1.65,-1.6), G=(0.45,-1.6), H=(3.75,-1.6), I=(2.1,0), J=(2.1,-3.2), K=(2.1,-1.6);
  5 KB (730 words) - 15:05, 15 January 2024
• 2006 AMC 12A Problems
  Sandwiches at Joe's Fast Food cost <math>3</math> dollars each and sodas cost <math>2</math> do ...B) \ } 32\qquad \mathrm{(C) \ } 33\qquad \mathrm{(D) \ } 34\qquad \mathrm{(E) \ } 35 </math>
  15 KB (2,223 words) - 13:43, 28 December 2020
• 2005 AMC 12A Problems
  ...B}) \ 2 \qquad (\mathrm {C})\ 5 \qquad (\mathrm {D}) \ 10 \qquad (\mathrm {E})\ 20 ...B}) \ -4 \qquad (\mathrm {C})\ 2 \qquad (\mathrm {D}) \ 4 \qquad (\mathrm {E})\ 8
  13 KB (1,971 words) - 13:03, 19 February 2020
• 2001 AMC 12 Problems
  The sum of two numbers is <math>S</math>. Suppose <math>3</math> is added to each number and then ...B)}\ 3S + 2\qquad \text{(C)}\ 3S + 6 \qquad\text{(D)} 2S + 6 \qquad \text{(E)}\ 2S + 12</math>
  13 KB (1,957 words) - 12:53, 24 January 2024
• 2003 AMC 12B Problems
  ...2}{3} \qquad \text {(C) } \frac{2}{3} \qquad \text {(D) } 1 \qquad \text {(E) } \frac{14}{3} ...y for two weeks. A green pill costs 1 dollar more than a pink pill, and Al's pills cost a total of 546 dollars for the two weeks. How much does one gree
  13 KB (1,987 words) - 18:53, 10 December 2022
• 2004 AMC 12B Problems
  ...hrm {B}) 6 \qquad (\mathrm {C}) 9 \qquad (\mathrm {D}) 12 \qquad (\mathrm {E}) 15</math> ...h>c\cdot a^b-d</math>, the values of <math>a</math>, <math>b</math>, <math>c</math>, and <math>d</math> are 0, 1, 2, and 3, although not necessarily in
  13 KB (2,049 words) - 13:03, 19 February 2020
• 2005 AMC 12B Problems
  \mathrm{(C)}\ 300 \qquad \mathrm{(E)}\ 500
  12 KB (1,781 words) - 14:59, 19 July 2024
• 2006 AMC 12B Problems/Problem 15
  ...B</math> are on the circle centered at <math> O</math>, and points <math> C</math> and <math> D</math> are on the circle centered at <math> P</math>, s pair A, B, C, D;
  3 KB (458 words) - 16:40, 6 October 2019
• 2006 AMC 12A Problems/Problem 20
  ...extbf{(C) } \frac{2}{243}\qquad \textbf{(D) } \frac{1}{81} \qquad \textbf{(E) } \frac{5}{243}</math> ...a new vertex next. Call this <math>C</math>. <math>A, B,</math> and <math>C</math> are always on the same plane.
  6 KB (1,079 words) - 22:48, 12 August 2024
• 2005 AMC 12B Problems/Problem 15
  \mathrm{(C)}\ 3 \qquad \mathrm{(E)}\ 5
  2 KB (411 words) - 21:02, 21 December 2020

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