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• Magic squares
  ''The Zen of Magic Squares, Circles, and Stars'' by Clifford A. Pickover
  666 bytes (109 words) - 22:53, 30 June 2021
• 2008 IMO Problems/Problem 1
  ...g their centers. We know that <math>H</math> is on the radical axis of the circles centered at <math>M_B</math> and <math>M_C</math>, so <math>A</math> is too
  2 KB (415 words) - 01:08, 19 November 2023
• 2011 IMO Problems/Problem 6
  Regardless, the circumcenter and an intersection of the circles are collinear with (0,0), so it is a tangency.
  2 KB (317 words) - 01:22, 19 November 2023
• 2000 AMC 8 Problems/Problem 19
  ...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 ...here <math>O</math> is the center of the semicircle. You have two quarter circles on top, and two quarter circle-sized "bites" on the bottom. Move the piece
  2 KB (383 words) - 16:58, 12 January 2024
• 1996 AJHSME Problems/Problem 25
  ...er circle meaning the set of points are equidistant from the center of the circles to the outside of the big circle.
  2 KB (270 words) - 20:03, 26 May 2021
• 1995 AJHSME Problems/Problem 9
  Three congruent circles with centers <math>P</math>, <math>Q</math>, and <math>R</math> are tangent If circle <math>Q</math> has diameter <math>4</math>, then so do congruent circles <math>P</math> and <math>R</math>. Draw a diameter through <math>P</math>
  2 KB (409 words) - 00:15, 5 July 2013
• 2008 AMC 8 Problems/Problem 18
  Two circles that share the same center have radii <math>10</math> meters and <math>20</
  2 KB (210 words) - 13:37, 19 October 2020
• Inscribe
  ...ircle. Any polygon can be inscribed in at most one circle (because any two circles can intersect at no more than two points), and any polygon can have at most
  732 bytes (123 words) - 05:35, 16 August 2011
• 1979 USAMO Problems/Problem 4
  ...and radius <math>\overline{PO}.</math> Lines <math>OA,OB</math> go to the circles <math>(O_1),(O_2)</math> passing through <math>P,O</math> and the line <mat
  3 KB (568 words) - 12:24, 11 March 2018
• 1996 AHSME Problems
  ...th>1</math> has center at <math>(5,0)</math>. A line is tangent to the two circles at points in the first quadrant. Which of the following is closest to the <
  15 KB (2,343 words) - 13:39, 19 February 2020
• 1996 AHSME Problems/Problem 18
  ...th>1</math> has center at <math>(5,0)</math>. A line is tangent to the two circles at points in the first quadrant. Which of the following is closest to the < The two circles are tangent to each other at the point <math>(4,0)</math>, since it is both
  2 KB (415 words) - 14:43, 5 June 2016
• 1996 AHSME Problems/Problem 27
  The spheres now become circles with centers at <math>(1,0)</math> and <math>(\frac{21}{2},0)</math>. They ...d <math>B</math> and third point at the first quadrant intersection of the circles. Let's call that altitude <math>h</math>.
  7 KB (1,046 words) - 11:42, 30 September 2023
• 1992 AJHSME Problems/Problem 24
  Four circles of radius <math>3</math> are arranged as shown. Their centers are the vert ...2=36</math>. The unshaded region of the square is composed of four quarter circles, and has the area of one circle, which is <math>9\pi</math>. The area of th
  1 KB (191 words) - 00:10, 5 July 2013
• 2010 PUMaC Problems
  Sterling draws 6 circles on the plane, which divide the plane into regions (including the unbounded Sterling draws 6 circles on the plane, which divide the plane into regions (including the unbounded
  22 KB (3,694 words) - 23:58, 3 June 2022
• 1950 AHSME Problems
  ...textbf{(D)}\ \text{Cuts neither axis}\qquad\\ \textbf{(E)}\ \text{Cuts all circles whose center is at the origin} </math>
  22 KB (3,306 words) - 19:50, 3 May 2023
• 2006 AMC 8 Problems/Problem 7
  ...th>. Circle <math> Z </math> has an area of <math> 9 \pi </math>. List the circles in order from smallest to the largest radius. Using the formulas of circles, <math> C=2 \pi r </math> and <math> A= \pi r^2 </math>, we find that circl
  868 bytes (153 words) - 19:35, 14 January 2024
• 1985 AHSME Problems
  ...\triangle ABC</math> with legs <math>5</math> and <math>12</math>, arcs of circles are drawn, one with center <math>A</math> and radius <math>12</math>, the o
  17 KB (2,488 words) - 03:26, 20 March 2024
• 1985 AHSME Problems/Problem 3
  ...\triangle ABC</math> with legs <math>5</math> and <math>12</math>, arcs of circles are drawn, one with center <math>A</math> and radius <math>12</math>, the o ...> and <math>BN = BC = 5</math> since they are both radii of the respective circles. Thus <math>MB = AB-AM = 13-12 = 1</math>, and so <math>MN = BN-BM = 5-1 =
  1 KB (207 words) - 18:40, 19 March 2024
• 2010 AMC 8 Problems
  ...of a <math>12</math>-inch pizza when placed. If a total of <math>24</math> circles of pepperoni are placed on this pizza without overlap, what fraction of the ...ne{AD}</math> has length <math>16</math>. What is the area between the two circles?
  18 KB (2,768 words) - 21:05, 9 January 2024
• 2010 AMC 8 Problems/Problem 10
  ...of a <math>12</math>-inch pizza when placed. If a total of <math>24</math> circles of pepperoni are placed on this pizza without overlap, what fraction of the ...c{12}{6} = 2</math>. From that we see that the area of the <math>24</math> circles of pepperoni is <math>\left ( \frac{2}{2} \right )^2 (24\pi) = 24\pi</math>
  955 bytes (141 words) - 23:55, 22 January 2024

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