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• 2002 AMC 12B Problems
  ...in a plane. What is the maximum number of points where at least two of the circles intersect?
  10 KB (1,547 words) - 04:20, 9 October 2022
• 2004 AMC 12B 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
  13 KB (2,049 words) - 13:03, 19 February 2020
• 2005 AMC 12B Problems
  ...h>1</math> foot. Each tile has a pattern consisting of four white quarter circles of radius <math>1/2</math> foot centered at each corner of the tile. The r
  12 KB (1,781 words) - 12:38, 14 July 2022
• 2006 AMC 12B Problems/Problem 15
  .../math> and <math> \overline{BC}</math> are common external tangents to the circles. What is the area of hexagon <math> AOBCPD</math>? ...> and <math>\angle ADP</math> are right angles due to being tangent to the circles, and the altitude creates <math>\angle OHD</math> as a right angle. <math>A
  3 KB (458 words) - 16:40, 6 October 2019
• 2006 AMC 12A Problems/Problem 13
  ...y tangent [[circle]]s, as shown. What is the sum of the areas of the three circles?
  1 KB (184 words) - 13:57, 19 January 2021
• 2006 AMC 12A Problems/Problem 16
  ...[[common internal tangent line | common internal tangent]] intersects the circles at <math>C</math> and <math>D</math>, respectively. Lines <math>AB</math> a
  2 KB (286 words) - 10:16, 19 December 2021
• 2006 AMC 12A Problems/Problem 19
  ...ctively. The equation of a common external [[tangent line|tangent]] to the circles can be written in the form <math>y=mx+b</math> with <math>m>0</math>. What
  2 KB (253 words) - 22:52, 29 December 2021
• 2005 AMC 12B Problems/Problem 5
  ...h>1</math> foot. Each tile has a pattern consisting of four white quarter circles of radius <math>1/2</math> foot centered at each corner of the tile. The r
  2 KB (223 words) - 14:30, 15 December 2021
• 2005 AMC 12B Problems/Problem 16
  ...in the coordinate plane. To find the circle enclosing these <math>4</math> circles, notice that if you connect the <math>4</math> centers as a square, the dia
  2 KB (364 words) - 04:54, 16 January 2023
• 2006 AMC 10A Problems
  ...le of radius 2. The sides of <math>\triangle ABC</math> are tangent to the circles as shown, and the sides <math>\overline{AB}</math> and <math>\overline{AC} ...and <math>8</math>, respectively. A common internal tangent intersects the circles at <math>C</math> and <math>D</math>, respectively. Lines <math>AB</math> a
  13 KB (2,028 words) - 16:32, 22 March 2022
• 2006 AMC 10A Problems/Problem 16
  ...<math>2</math>. The sides of <math>\triangle ABC</math> are tangent to the circles as shown, and the sides <math>\overline{AB}</math> and <math>\overline{AC} Let the centers of the smaller and larger circles be <math>O_1</math> and <math>O_2</math> , respectively.
  5 KB (732 words) - 23:19, 19 September 2023
• 2005 AIME II Problems
  ...math> C_2 </math> are 4 and 10, respectively, and the centers of the three circles are all collinear. A chord of <math> C_3 </math> is also a common external Let <math> w_1 </math> and <math> w_2 </math> denote the circles <math> x^2+y^2+10x-24y-87=0 </math> and <math> x^2 +y^2-10x-24y+153=0, </ma
  7 KB (1,119 words) - 21:12, 28 February 2020
• 2005 AIME II Problems/Problem 8
  ...> C_2 </math> are 4 and 10, respectively, and the [[center]]s of the three circles are all [[collinear]]. A [[chord]] of <math> C_3 </math> is also a common e ...e the centers and <math>r_1 = 4, r_2 = 10,r_3 = 14</math> the radii of the circles <math>C_1, C_2, C_3</math>. Let <math>T_1, T_2</math> be the points of tang
  4 KB (693 words) - 13:03, 28 December 2021
• Problem solving
  ...from another school asked me for my formula sheets. In my local and state circles, students’ formula sheets were the source of knowledge, the source of pow
  6 KB (1,039 words) - 17:43, 30 July 2018
• Mathematician
  Contrary to the belief in some circles, "mathematician" is not synonymous with "professor of mathematics", althoug
  918 bytes (123 words) - 10:42, 30 July 2006
• 2005 AIME I Problems
  ...e area of the region inside circle <math> C </math> and outside of the six circles in the ring. Find <math> \lfloor K \rfloor. </math>
  6 KB (983 words) - 05:06, 20 February 2019
• 2005 AIME I Problems/Problem 1
  ...e area of the region inside circle <math> C </math> and outside of the six circles in the ring. Find <math> \lfloor K \rfloor</math> (the [[floor function]]). Define the radii of the six congruent circles as <math>r</math>. If we draw all of the radii to the points of external ta
  1 KB (213 words) - 13:17, 22 July 2017
• 2005 AIME II Problems/Problem 15
  ...th> have center <math>(x,y)</math> and radius <math>r</math>. Now, if two circles with radii <math>r_1</math> and <math>r_2</math> are externally tangent, th .... In particular, the locus of points <math>C</math> that can be centers of circles must be an ellipse with foci <math>F_1</math> and <math>F_2</math> and majo
  12 KB (2,000 words) - 13:17, 28 December 2020
• 2004 AIME I Problems/Problem 4
  ...>. Thus, they enclose the area of the square minus the area of the quarter circles, which is <math>4-\pi \approx 0.86</math>, so <math>100k = \boxed{086}</mat
  3 KB (532 words) - 09:22, 11 July 2023
• 2004 AIME II Problems/Problem 12
  ...circle contained within the trapezoid is [[tangent]] to all four of these circles. Its radius is <math> \frac{-k+m\sqrt{n}}p, </math> where <math> k, m, n, <
  3 KB (431 words) - 23:21, 4 July 2013

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