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• 2000 AMC 8 Problems
  ...und the region shown. Arcs <math>AB</math> and <math>AD</math> are quarter-circles, and arc <math>BCD</math> is a semicircle. What is the area, in square unit
  15 KB (2,165 words) - 18:29, 5 June 2024
• 2009 AIME II Problems/Problem 5
  ...gent to circle <math>A</math> at the other two vertices of <math>T</math>. Circles <math>B</math>, <math>C</math>, and <math>D</math> are all externally tange ...B</math> and <math>E</math>, and <math>Y</math> be the intersection of the circles with centers <math>C</math> and <math>E</math>. Since the radius of <math>B
  2 KB (372 words) - 20:54, 9 August 2020
• 2009 USAMO Problems/Problem 1
  Given circles <math>\omega_1</math> and <math>\omega_2</math> intersecting at points <mat
  2 KB (290 words) - 13:16, 17 April 2021
• Radical axis
  ...ical axis is the line that one gets when you subtract the equations of two circles). a. The radical axis is a line perpendicular to the line connecting the circles' centers (line <math>l</math>).
  12 KB (2,125 words) - 08:38, 23 May 2024
• 1964 IMO Problems
  ...es, a circle is inscribed. Find the sum of the areas of all four inscribed circles (in terms of <math>a,b,c</math>).
  3 KB (414 words) - 12:38, 29 January 2021
• 1964 IMO Problems/Problem 3
  ...es, a circle is inscribed. Find the sum of the areas of all four inscribed circles (in terms of <math>a,b,c</math>).
  2 KB (414 words) - 12:48, 29 January 2021
• 1967 IMO Problems
  ...alpha </math>. If <math>\triangle ABD</math> is acute, prove that the four circles of radius <math>1</math> with centers <math>A</math>, <math>B</math>, <math
  3 KB (522 words) - 12:40, 29 January 2021
• Asymptote: Drawing
  ==Circles== ...everal useful pre defined paths for drawing things like unit squares, unit circles, etc. Just use the unit- paths!
  3 KB (433 words) - 22:13, 26 April 2024
• 2009 USAMO Problems
  Given circles <math>\omega_1</math> and <math>\omega_2</math> intersecting at points <mat
  4 KB (718 words) - 18:16, 17 September 2012
• Asymptote: Graphing
  Remember, you can still draw normal functions, so you can create lines, circles and ellipses.
  2 KB (299 words) - 17:09, 15 March 2016
• 1992 AJHSME Problems
  Four circles of radius <math>3</math> are arranged as shown. Their centers are the vert
  17 KB (2,346 words) - 13:36, 19 February 2020
• Constructible number
  *(E) Finding the intersection point(s) of two previously constructed circles. *(iii) <math>\theta</math> is the intersection of circles with centers <math>z</math> and <math>z'</math> and radii <math>r</math> an
  8 KB (1,305 words) - 08:39, 21 August 2009
• 2010 AMC 10B Problems
  Two circles lie outside regular hexagon <math>ABCDEF</math>. The first is tangent to <m
  12 KB (1,817 words) - 22:44, 22 December 2020
• Mock AIME 1 2010 Problems
  Let <math>\omega_1</math> and <math>\omega_2</math> be circles of radii 5 and 7, respectively, and suppose that the distance between their
  7 KB (1,297 words) - 01:29, 25 November 2016
• 2010 AIME I Problems/Problem 15
  14 KB (2,210 words) - 13:14, 11 January 2024
• 2010 AIME II Problems/Problem 15
  ...}{54}=\frac{b^2z}{58}</math>. This equation determines the radical axis of circles <math>ANM</math> and <math>AED</math>, on which points <math>P</math> and <
  9 KB (1,523 words) - 15:24, 21 November 2023
• 1995 AJHSME Problems
  Three congruent circles with centers <math>P</math>, <math>Q</math>, and <math>R</math> are tangent
  14 KB (2,096 words) - 18:29, 2 January 2023
• 2007 AMC 8 Problems/Problem 25
  ...math>. The larger sections trisect a "ring" which is the difference of two circles, one with radius <math>3</math>, the other radius <math>6</math>. So, the a
  3 KB (510 words) - 10:08, 18 June 2024
• 2010 AMC 12B Problems/Problem 18
  ...either circle's center (symmetry, you chose!). The intersection of the two circles should form a geometrical lens shape. By sectors, ...}{2}x^2</math> and <math>x^2</math> are tangent. The area ratio of the two circles is <cmath>\frac{\pi}{4\pi} = \boxed{\frac{1}{4} \text{(C)}}</cmath>.
  6 KB (1,105 words) - 13:39, 9 January 2024
• 1969 IMO Problems
  ...he perpendicular from <math>C</math> to <math>AB</math>. We consider three circles, <math>\gamma_1, \gamma_2, \gamma_3</math>, all tangent to the line <math>A
  3 KB (428 words) - 13:34, 29 January 2021

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