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

• 2004 AIME II Problems
  ...h> A 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, <
  9 KB (1,410 words) - 05:05, 20 February 2019
• 1983 AIME Problems
  In the adjoining figure, two circles with radii <math>8</math> and <math>6</math> are drawn with their centers <
  7 KB (1,104 words) - 03:13, 27 May 2024
• 1984 AIME Problems
  ...one side of the line is equal to the total area of the parts of the three circles to the other side of it. What is the absolute value of the slope of this li
  6 KB (933 words) - 01:15, 19 June 2022
• 1993 AIME Problems
  ...</math>. Let <math>R\,</math> and <math>S\,</math> be the points where the circles inscribed in the triangles <math>ACH\,</math> and <math>BCH^{}_{}</math> ar
  8 KB (1,275 words) - 06:55, 2 September 2021
• 1995 AIME Problems
  ...th>9</math> has a chord that is a common external tangent of the other two circles. Find the square of the length of this chord.
  6 KB (1,000 words) - 00:25, 27 March 2024
• 1997 AIME Problems
  Circles of radii 5, 5, 8, and <math>m/n</math> are mutually externally tangent, whe
  7 KB (1,098 words) - 17:08, 25 June 2020
• 2002 AIME I Problems
  ...congruent circles arranged in three rows and enclosed in a rectangle. The circles are tangent to one another and to the sides of the rectangle as shown in th
  8 KB (1,374 words) - 21:09, 27 July 2023
• 2003 AIME I Problems
  ...circle of radius 1 is colored red, and each region bounded by consecutive circles is colored either red or green, with no two adjacent regions the same color
  6 KB (965 words) - 16:36, 8 September 2019
• 2002 AIME II Problems
  ...he line <math>y = mx</math>, where <math>m > 0</math>, are tangent to both circles. It is given that <math>m</math> can be written in the form <math>a\sqrt {b
  7 KB (1,177 words) - 15:42, 11 August 2023
• 2003 AIME II Problems
  Find 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 <m
  7 KB (1,127 words) - 09:02, 11 July 2023
• 1983 AIME Problems/Problem 14
  In the adjoining figure, two circles with radii <math>8</math> and <math>6</math> are drawn with their centers < ...math>QP = PR = x</math>. Extend the line containing the centers of the two circles to meet <math>R</math>, and to meet the other side of the large circle at a
  13 KB (2,151 words) - 17:48, 27 May 2024
• 1984 AIME Problems/Problem 6
  ...side of the line is equal to the total [[area]] of the parts of the three circles to the other side of it. What is the [[absolute value]] of the [[slope]] of ...e [[midpoint]] of <math>\overline{AC}</math> (the centers of the other two circles), and call it <math>M</math>. If we draw the feet of the [[perpendicular]]s
  6 KB (1,022 words) - 19:29, 22 January 2024
• 2006 AMC 10B Problems/Problem 4
  Circles of diameter <math>1</math> inch and <math>3</math> inches have the same cen
  1 KB (172 words) - 10:47, 19 December 2021
• 1991 AIME Problems/Problem 12
  ...en we found <math>AP</math>, the segment <math>OB</math> is tangent to the circles with diameters <math>AO,CO</math>.
  8 KB (1,270 words) - 23:36, 27 August 2023
• 1991 AIME Problems/Problem 11
  ...es must be tangent on the larger circle. Now consider two adjacent smaller circles. This means that the line connecting the radii is a segment of length <math ...3})^{2} = \pi (7 - 4 \sqrt {3})</math>, so the area of all <math>12</math> circles is <math>\pi (84 - 48 \sqrt {3})</math>, giving an answer of <math>84 + 48
  4 KB (740 words) - 17:46, 24 May 2024
• 1992 AIME Problems/Problem 10
  ...ique area of the two circles. We can do this by adding the area of the two circles and then subtracting out their overlap. There are two methods of finding th 2. Consider that the circles can be converted into polar coordinates, and their equations are <math>r =
  2 KB (323 words) - 12:05, 16 July 2019
• 2006 AMC 10B Problems/Problem 24
  ...at <math>AD</math> and <math>BC</math> are common external tangents to the circles. What is the area of the [[concave]] [[hexagon]] <math>AOBCPD</math>?
  4 KB (558 words) - 14:38, 6 April 2024
• 1993 AIME Problems/Problem 15
  ...</math>. Let <math>R\,</math> and <math>S\,</math> be the points where the circles inscribed in the triangles <math>ACH\,</math> and <math>BCH^{}_{}</math> ar
  3 KB (449 words) - 21:39, 21 September 2023
• 1994 AIME Problems/Problem 15
  ...he respective conditions for <math>P</math> is the region inside the (semi)circles with diameters <math>\overline{AB}, \overline{BC}, \overline{CA}</math>. ...</math> (shaded region below) is simply the sum of two [[segment]]s of the circles. If we construct the midpoints of <math>M_1, M_2 = \overline{AB}, \overline
  4 KB (717 words) - 22:20, 3 June 2021
• 1995 AIME Problems/Problem 4
  ...th>9</math> has a chord that is a common external tangent of the other two circles. Find the square of the length of this chord. We label the points as following: the centers of the circles of radii <math>3,6,9</math> are <math>O_3,O_6,O_9</math> respectively, and
  3 KB (605 words) - 11:30, 5 May 2024

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