Create the page "Circles" on this wiki! See also the search results found.

• 1998 AHSME Problems
  Let <math>R</math> be a rectangle. How many circles in the plane of <math>R</math> have a diameter both of whose endpoints are
  15 KB (2,222 words) - 10:40, 11 August 2020
• 1988 IMO Problems/Problem 1
  Consider 2 concentric circles with radii <math>R</math> and <math>r</math> (<math>R>r</math>) with center
  3 KB (545 words) - 11:32, 30 January 2021
• 1984 IMO Problems/Problem 4
  ...MT = \frac{1}{2} AM \cdot UN</math> because of the equivalence of radii in circles. Hence <math>[ANM] = [DMN]</math>, so <math>A</math> and <math>D</math> are
  4 KB (750 words) - 23:49, 29 January 2021
• 1989 IMO Problems/Problem 4
  ...ion of circle <math>B</math> with the line <math>AB</math>. Thus, the two circles are externally tangent to each other. ...reasoning that we found circles <math>A,B</math> are tangent, we find that circles <math>P,A</math> and <math>P,B</math> are externally tangent also.
  4 KB (771 words) - 11:57, 30 January 2021
• 1995 IMO Problems/Problem 1
  ...<math>A,B,C,D</math> be four distinct points on a line, in that order. The circles with diameters <math>AC</math> and <math>BD</math> intersect at <math>X</ma ...h>BD</math> is line <math>DN</math>. Since the pairwise radical axes of 3 circles are concurrent, we have <math>AM,DN,XY</math> are concurrent as desired.
  5 KB (854 words) - 05:48, 4 September 2024
• 2000 USAMO Problems
  ...passing through <math>A_1</math> and <math>A_2.</math> Suppose there exist circles <math>\omega_2, \omega_3, \dots, \omega_7</math> such that for <math>k = 2,
  3 KB (495 words) - 19:02, 18 April 2014
• 2000 USAMO Problems/Problem 5
  ...passing through <math>A_1</math> and <math>A_2.</math> Suppose there exist circles <math>\omega_2, \omega_3, \dots, \omega_7</math> such that for <math>k = 2, ...heta_{1} = \theta_{7}</math> implies that <math>O_1 \equiv O_7</math>, and circles <math>\omega_1</math> and <math>\omega_7</math> are the same circle since t
  3 KB (609 words) - 09:52, 20 July 2016
• 2008 iTest Problems
  ...in a plane. What is the maximum number of points where at least two of the circles intersect?'' Tony realizes that he can draw the four circles such that each pair of circles intersects in two points. After careful doodling, Tony finds the correct an
  71 KB (11,749 words) - 01:31, 2 November 2023
• Spiral similarity
  ===Common point for 6 circles=== ...math> so these circles contain point <math>O</math>. Similarly for another circles.
  28 KB (4,863 words) - 00:29, 16 December 2023
• 2002 AMC 10A Problems
  ...t circle is tangent to the six circles that surround it, and each of those circles is tangent to the large circle and to its small-circle neighbors. Find the
  12 KB (1,813 words) - 21:39, 19 July 2024
• 2002 AMC 10B Problems
  Circles of radius <math>2</math> and <math>3</math> are externally tangent and are ...in a plane. What is the maximum number of points where at least two of the circles intersect?
  10 KB (1,539 words) - 13:34, 23 July 2024
• 2002 AMC 12A Problems/Problem 7
  Let <math>r_1</math> and <math>r_2</math> be the radii of circles <math>A</math> and<math> B</math>, respectively. ...rough and simplify to get <math>\frac{r_1}{r_2}=\frac{2}{3}</math>. As all circles are similar to one another, the ratio of the areas is just the square of th
  3 KB (505 words) - 00:51, 26 July 2024
• 2004 AMC 10B Problems
  An annulus is the region between two concentric circles. The concentric circles in the figure have radii <math>b</math> and <math>c</math>, with <math>b>c Three circles of radius <math>1</math> are externally tangent to each other and internall
  14 KB (2,137 words) - 15:29, 9 June 2024
• 1975 USAMO Problems/Problem 4
  ...<math>AB</math> passing through <math>P</math> and terminating on the two circles such that <math>AP\cdot PB</math> is a maximum. Let <math>E</math> and <math>F</math> be the centers of the small and big circles, respectively, and <math>r</math> and <math>R</math> be their respective ra
  2 KB (410 words) - 15:13, 13 August 2014
• 1962 IMO Problems/Problem 6
  ...e. Prove that the distance <math>d</math> between the centers of these two circles is
  2 KB (308 words) - 06:29, 16 December 2023
• 1962 IMO Problems/Problem 7
  In order for these two circles to be part of the same sphere and also tangent to line <math>AB</math>, the The only way these to circles can share the same tangent point on edge <math>AB</math> is if <math>|AP_{A
  11 KB (1,928 words) - 20:52, 21 November 2023
• 1963 IMO Problems/Problem 2
  ...<math>X</math>, the total locus is the union of the circumferences of all circles that have a diameter <math>AX</math>, where <math>X</math> is some point on
  2 KB (306 words) - 04:49, 19 February 2019
• 1975 USAMO Problems
  ...<math>AB</math> passing through <math>P</math> and terminating on the two circles such that <math>AP\cdot PB</math> is a maximum.
  2 KB (332 words) - 18:57, 3 July 2013
• 2021 GMC 10B
  ...grid has 16 circles with radius of <math>\frac{1}{2}</math> such that all circles have vertices of the square as center. Assume that the diagram continues on
  11 KB (1,695 words) - 14:33, 7 March 2022
• 1998 AHSME Problems/Problem 23
  Both sets of points are quite obviously circles. To show this, we can rewrite each of them in the form <math>(x-x_0)^2 + (y ...distance between the two centers is <math>5</math>, and therefore the two circles intersect if <math>2\leq r \leq 12</math>.
  1 KB (193 words) - 09:12, 2 December 2018

View (previous 20 | next 20) (20 | 50 | 100 | 250 | 500)