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• Circle
  A circle is defined as the or [[locus]] of [[point]]s in a [[plane]] with an equal distance from a fixed point called the [[center]]. This distance from ...h [[side]]s as either [[secant line|secants]] or [[tangent line|tangent]]s of the circle.
  9 KB (1,510 words) - 19:56, 16 January 2025
• Polygon
  ...nar figure]] consisting of straight [[line segment]]s. There are two types of polygons: [[convex polygon|convex]] and [[concave polygon|concave]]. In their most general form, polygons are an ordered [[set]] of [[vertex|vertices]], <math>\{A_1, A_2, \ldots, A_n\}</math>, <math>n \geq 3
  2 KB (372 words) - 19:04, 30 May 2015
• Law of Cosines
  ...riangles with two sides and an include angle are [[congruent]] by the Side-Angle-Side congruence postulate. ...e <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
• Geometry
  ...ng with figures in a given [[space]]. It is one of the two oldest branches of mathematics, along with [[arithmetic]] (which eventually branched into [[nu ...collegiate]] [[mathematics competitions]] is Euclidean geometry. This type of geometry was first formally outlined by the Greek [[mathematician]] [[Eucli
  3 KB (478 words) - 01:52, 25 August 2024
• Area
  ...he size of the region that a two-[[dimension]]al figure occupies. The size of a region in higher dimensions is referred to as [[volume]]. ...ary means. One can find the area of even more complex regions via the use of [[calculus]].
  7 KB (1,185 words) - 20:48, 25 November 2024
• Right triangle
  ...riangle''' is any [[triangle]] with an [[interior angle|interior]] [[right angle]]. ...se is labeled <math>c</math>. The other two sides are called the [[leg]]s of the triangle, labeled <math>a</math> and <math>b</math>.
  4 KB (543 words) - 19:37, 31 January 2025
• 2002 AMC 12A Problems
  Compute the sum of all the roots of ...stead, she subtracted 9 and then divided the result by 3, giving an answer of 43. What would her answer have been had she worked the problem correctly?
  12 KB (1,792 words) - 13:06, 19 February 2020
• 2006 AMC 12A Problems/Problem 17
  ...line{BE}</math>. Point <math>F</math> lies on the circle, on the same side of <math>\overline{BE}</math> as <math>A</math>. Segment <math>AF</math> is ta ...h>B, D</math>, and <math>E</math> are [[collinear]] and contain a diagonal of <math>ABCD</math>. The [[Pythagorean theorem]] results in
  6 KB (958 words) - 23:29, 28 September 2023
• 1984 AIME Problems
  ...8}</math> if <math>a_1</math>, <math>a_2</math>, <math>a_3\ldots</math> is an arithmetic progression with common difference 1, and <math>a_1+a_2+a_3+\ldo ...is the smallest positive multiple of <math>15</math> such that every digit of <math>n</math> is either <math>8</math> or <math>0</math>. Compute <math>\f
  6 KB (933 words) - 01:15, 19 June 2022
• 1995 AIME Problems
  ...s of square <math>S_{i+2}.</math> The total area enclosed by at least one of <math>S_{1}, S_{2}, S_{3}, S_{4}, S_{5}</math> can be written in the form < Find the last three digits of the product of the positive roots of
  6 KB (1,000 words) - 00:25, 27 March 2024
• 2001 AIME I Problems
  Find the sum of all positive two-digit integers that are divisible by each of their digits. ...th>27</math> more than the mean of <math>\mathcal{S}</math>. Find the mean of <math>\mathcal{S}</math>.
  7 KB (1,220 words) - 14:05, 24 November 2024
• 1983 AIME Problems/Problem 14
  ...math> and <math>PR</math> have equal length. Find the square of the length of <math>QP</math>. ...intersects the small circle. This fact can be derived from the application of the Midpoint Theorem to the trapezoid made by dropping perpendiculars from
  14 KB (2,351 words) - 21:06, 8 December 2024
• 1990 AIME Problems/Problem 14
  ...d]], all four of whose faces are [[isosceles triangle]]s. Find the volume of this pyramid. ...base <math>12\sqrt{3} - 13\sqrt{3} - 13\sqrt{3} \triangle</math>. The area of this isosceles triangle is easy to find by <math>[ACD] = \frac{1}{2}bh</mat
  8 KB (1,148 words) - 22:35, 4 February 2025
• 1997 AIME Problems/Problem 6
  ...>A_1</math>, <math>A_n</math>, and <math>B</math> are consecutive vertices of a regular polygon? ...0}{n}</math>, <math>\angle A_nA_1B = \frac{(m-2)180}{m}</math>, and <math>\angle A_2A_1B = 60^{\circ}</math>. Since those three angles add up to <math>360^{
  3 KB (497 words) - 00:39, 22 December 2018
• 2000 AIME I Problems/Problem 14
  ...QB = BC.</math> Angle <math>ACB</math> is <math>r</math> times as large as angle <math>APQ,</math> where <math>r</math> is a positive real number. Find <mat ...h>AP=QB</math>, it also follows that <math>AQ=PC</math>. Now apply the Law of Sines to triangle <math>PBC</math> to find <cmath>\frac{\sin 3x}{BC}=\frac{
  9 KB (1,505 words) - 23:17, 31 December 2024
• 2001 AIME I Problems/Problem 4
  ...> are positive integers, and <math>c</math> is not divisible by the square of any prime. Find <math>a+b+c</math>. ...<math>\angle TCA=75^{\circ}</math>, meaning <math>\triangle TAC</math> is an isosceles triangle and <math>AC=24</math>.
  5 KB (779 words) - 23:17, 10 December 2024
• 2003 AIME I Problems/Problem 10
  ...math> \angle MCA = 23^\circ. </math> Find the number of degrees in <math> \angle CMB. </math> ...triangle ABC</math> such that <math>\angle CBN = 7^\circ</math> and <math>\angle BCN = 23^\circ</math>.
  7 KB (1,082 words) - 02:08, 30 September 2024
• Equilateral triangle
  ...e. Since a triangle has a total of <math>180</math> degrees, each angle of an equilateral triangle has <math>60</math> degrees. ...ral triangle is the simplest [[regular polygon]]. It is also the only type of [[polygon]] that such that the [[equilateral]] polygon must also be the [[e
  1 KB (186 words) - 19:57, 15 September 2022
• Volume
  The '''volume''' of an object is a [[measure]] of the [[amount]] of [[space]] that it occupies. Note that volume only applies to three-[[dimens This section covers the methods to find volumes of common [[Euclidean]] objects.
  3 KB (523 words) - 20:24, 17 August 2023
• Right angle
  ...dicular]] [[line]]s. The [[measure of an angle | measure]] of every right angle is 90 [[degree (geometry) | degrees]] or <math>\frac \pi 2</math> [[radian] * [[Angle]]
  673 bytes (91 words) - 23:59, 11 June 2022

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