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• Geometric inequality
  ...[[area]] <math>A</math> and [[perimeter]] <math>P</math>, then <math>\frac{4\pi A}{P^2} \le 1</math>. This means that given a perimeter <math>P</math> f ...math>, <math>AB\cdot CD+BC\cdot DA\ge AC\cdot BD</math> with equality when quadrilateral <math>ABCD</math> is cyclic.
  7 KB (1,300 words) - 01:11, 28 October 2024
• Brahmagupta's Formula
  ...a's Formula''' is a [[formula]] for determining the [[area]] of a [[cyclic quadrilateral]] given only the four side [[length]]s, given as follows: <cmath>[ABCD] = \ <cmath>4[ABCD]^2=\sin^2 B(ab+cd)^2</cmath>
  3 KB (543 words) - 19:35, 29 October 2024
• Ptolemy's theorem
  ...es a relationship between the side lengths and the diagonals of a [[cyclic quadrilateral]]; it is the [[equality condition | equality case]] of [[Ptolemy's Inequali Given a [[cyclic quadrilateral]] <math>ABCD</math> with side lengths <math>{a},{b},{c},{d}</math> and [[di
  6 KB (922 words) - 17:34, 13 January 2025
• 1970 IMO Problems/Problem 6
  ...st <math>3</math> replaced by <math>4</math>. Hence at most <math>\frac{3}{4}</math> of the <math>10</math>, or <math>7.5</math>, can be acute, and henc We start by proving that a <math>4</math>-gon has <math>4</math> triangles, out of which
  6 KB (1,054 words) - 18:09, 11 December 2024
• Square (geometry)
  A '''square''' is a [[quadrilateral]] in which all [[edge|sides]] have equal length and all [[angle | angles]] draw(A--B--C--D--cycle, StickIntervalMarker(4));
  1 KB (170 words) - 18:31, 3 September 2024
• Polygon
  | [[quadrilateral|4]]
  2 KB (372 words) - 19:04, 30 May 2015
• Bretschneider's formula
  Suppose we have a [[quadrilateral]] with [[edge]]s of length <math>a,b,c,d</math> (in that order) and [[diago <math>[ABCD]=\frac{1}{4} \cdot \sqrt{4p^2q^2-(b^2+d^2-a^2-c^2)^2}</math>.
  3 KB (566 words) - 03:51, 12 February 2021
• Law of Cosines
  draw(D--(30,4)--(34,4)--(34,0)--D); 1. If the sides of a triangle have lengths 2, 3, and 4, what is the radius of the circle circumscribing the triangle?
  6 KB (1,003 words) - 00:02, 20 May 2024
• Law of Sines
  pair A=(-1,5), B=(-4,-1), C=(4,-1), D, O; *If the sides of a triangle have lengths 2, 3, and 4, what is the radius of the circle circumscribing the triangle?
  4 KB (658 words) - 21:52, 4 February 2025
• Area
  ...circ}</math> and the area of the entire polygon is <math>\frac{n\cdot s^2}{4} \cot\frac{180}{n}^{\circ}</math>. * <math>\frac{1}{K}=4\sqrt{H(H-h_a^{-1})(H-h_b^{-1})(H-h_c^{-1})}</math>, where <math>H=\frac{(h_
  7 KB (1,185 words) - 20:48, 25 November 2024
• 1985 IMO Problems/Problem 5
  <math>M</math> is the Miquel Point of quadrilateral <math>ACNK</math>, so there is a spiral similarity centered at <math>M</mat <math>M</math> is the Miquel Point of quadrilateral <math>ACNK,</math> so <math>MO''O'O</math> is cyclic.
  3 KB (496 words) - 13:35, 18 January 2023
• Rectangle
  A '''rectangle''' is a [[quadrilateral]] in which all [[angle]]s are [[right angle]]s. dot("$A$",A,1.5*dir(A),linewidth(4));
  782 bytes (108 words) - 13:36, 6 March 2022
• Parallelogram
  A '''parallelogram''' is a [[quadrilateral]] in which both pairs of opposite sides are parallel. Its properties inclu ...onals together divide the figure into 2 pairs of congruent triangles. All 4 triangles have an equal area.
  910 bytes (122 words) - 21:48, 13 November 2024
• Rhombus
  ...s''' is a geometric figure that lies in a [[plane]]. It is defined as a [[quadrilateral]] all of whose sides are [[congruent (geometry) | congruent]]. It is a spe * Its diagonals divide the figure into 4 congruent [[triangle]]s.
  3 KB (490 words) - 15:30, 22 February 2024
• 2006 AIME I Problems
  In quadrilateral <math> ABCD , \angle B </math> is a right angle, diagonal <math> \overline{ == Problem 4 ==
  7 KB (1,173 words) - 03:31, 4 January 2023
• 2021 JMC 10
  ...bf{(A) } 1 \qquad\textbf{(B) } 2 \qquad\textbf{(C) } 3 \qquad\textbf{(D) } 4 \qquad\textbf{(E) } 7</math> ==Problem 4==
  12 KB (1,784 words) - 16:49, 1 April 2021
• 2001 AMC 12 Problems
  == Problem 4 == [[2001 AMC 12 Problems/Problem 4|Solution]]
  13 KB (1,957 words) - 12:53, 24 January 2024
• 2002 AMC 12B Problems
  \qquad\mathrm{(C)}\ 4 when <math>x=4</math>?
  10 KB (1,547 words) - 04:20, 9 October 2022
• 2006 AMC 10A Problems
  == Problem 4 == [[2006 AMC 10A Problems/Problem 4|Solution]]
  13 KB (2,028 words) - 16:32, 22 March 2022
• 2006 AMC 10A Problems/Problem 17
  ...addition, <math>AH=AC=2</math>, and <math>AD=3</math>. What is the area of quadrilateral <math>WXYZ</math> shown in the figure? === Solution 4 ===
  6 KB (1,106 words) - 10:20, 4 November 2024

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