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• Ptolemy's theorem
  ...ath>, <math>AC=8</math>, <math>BC=9</math>. Point <math>D</math> is on the circumscribed circle of the triangle so that <math>AD</math> bisects angle <math>BAC</mat
  6 KB (922 words) - 17:34, 13 January 2025
• Law of Sines
  4 KB (658 words) - 21:52, 4 February 2025
• 2003 AMC 12A Problems
  ...e circumscribed about the square and <math>B</math> the area of the circle circumscribed around the triangle. Find <math>A/B</math>.
  13 KB (1,955 words) - 21:06, 19 August 2023
• 2005 AMC 12B Problems/Problem 18
  ...h> as the hypotenuse. Note <math>C</math> cannot be inside this triangle's circumscribed circle or else <math>\angle C > 90^\circ</math>. Hence, the area of <math>R
  2 KB (262 words) - 21:20, 21 December 2020
• 2003 AIME II Problems
  ...the area of rhombus <math>ABCD</math> given that the radii of the circles circumscribed around triangles <math>ABD</math> and <math>ACD</math> are <math>12.5</math
  7 KB (1,127 words) - 09:02, 11 July 2023
• 1991 AIME Problems/Problem 11
  ...regular dodecagon whose vertices are the centers of the smaller triangles circumscribed about a circle of radius <math>1</math>.
  4 KB (740 words) - 17:46, 24 May 2024
• Circumcenter
  ...r]] of the [[circumcircle]] of a [[polygon]]. Only certain polygons can be circumscribed by a [[circle]]: all [[nondegenerate]] [[triangle]]s have a circumcircle w
  2 KB (390 words) - 14:14, 22 November 2024
• Cube (geometry)
  2 KB (244 words) - 11:04, 24 April 2023
• Apothem
  ...en the number of sides, <math>n</math>, and radius of the [[circumcircle | circumscribed circle]], <math>R</math>, the length of the apothem is <math>R\cos\left(\fr
  1 KB (171 words) - 18:33, 3 September 2024
• Euler line
  ...he radical axes of the de Longchamps circle <math>\omega</math> and of the circumscribed circle <math>\Omega</math> of <math>\triangle ABC.</math>
  59 KB (10,203 words) - 04:47, 30 August 2023
• 2003 AMC 10A Problems
  ...quilateral triangle equals the number of square inches in the area of its circumscribed circle. What is the radius, in inches, of the circle?
  13 KB (1,900 words) - 22:27, 6 January 2021
• 2003 AMC 10A Problems/Problem 17
  ...quilateral triangle equals the number of square inches in the area of its circumscribed circle. What is the radius, in inches, of the circle? <!-- don't remove the
  2 KB (414 words) - 13:48, 4 April 2024
• 2005 Cyprus Seniors TST/Day 1/Problem 3
  (i) The circumscribed circles of the triangles <math>PP_{1}\Delta</math> and <math>PP_{2}\Gamma</
  2 KB (294 words) - 15:12, 17 December 2006
• Mock AIME 4 2006-2007 Problems
  ...length 43, 13, and 48, respectively. Let <math>\omega</math> be the circle circumscribed around <math>\triangle ABC</math> and let <math>D</math> be the intersectio
  6 KB (923 words) - 14:17, 16 January 2007
• Mock AIME 4 2006-2007 Problems/Problem 15
  5 KB (734 words) - 14:46, 27 December 2024
• 1960 IMO Problems
  ...on 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 in the base of the cone. Le
  3 KB (511 words) - 21:21, 20 August 2020
• 2004 USAMO Problems
  Let <math>ABCD </math> be a [[quadrilateral]] circumscribed about a circle, whose interior and exterior angles are at least <math>60 ^{
  3 KB (474 words) - 09:20, 14 May 2021
• 1989 USAMO Problems
  ...of triangle <math>ABC</math> and point <math>O</math> is the center of the circumscribed circle, prove that line <math>IO</math> intersects segments <math>AB</math>
  2 KB (326 words) - 18:52, 18 July 2016
• Pascal's Theorem
  ...ual, [[Brianchon's Theorem]], which states that the diagonals of a hexagon circumscribed about a conic concur. ...math> \ell_A, \ell_B, \ell_C </math> can be the tangent lines to any conic circumscribed about triangle <math>ABC </math> and the result still holds.
  5 KB (833 words) - 15:23, 6 July 2024
• 2007 AMC 12B Problems/Problem 3
  The point <math>O</math> is the center of the circle circumscribed about triangle <math>ABC</math>, with <math>\angle BOC = 120^{\circ}</math>
  905 bytes (130 words) - 10:39, 27 February 2022

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