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• 2014 AMC 10B Problems/Problem 19
  Two concentric circles have radii <math>1</math> and <math>2</math>. Two points on the outer circl Let the center of the two circles be <math>O</math>. Now pick an arbitrary point <math>A</math> on the bounda
  2 KB (383 words) - 19:44, 28 April 2021
• 1993 AHSME Problems/Problem 8
  ...of radius 1 that are in the same plane and tangent to each other. How many circles of radius 3 are in this plane and tangent to both <math>C_1</math> and <mat ...other touching the bottoms and encircling upward. There are two radius 3 circles passing through the point where <math>C_1</math> and <math>C_2</math> are t
  1 KB (208 words) - 20:59, 27 May 2021
• 1992 AHSME Problems/Problem 11
  The ratio of the radii of two concentric circles is <math>1:3</math>. If <math>\overline{AC}</math> is a diameter of the lar
  2 KB (324 words) - 12:02, 24 November 2016
• 1992 AHSME Problems
  The ratio of the radii of two concentric circles is <math>1:3</math>. If <math>\overline{AC}</math> is a diameter of the lar
  16 KB (2,548 words) - 13:40, 19 February 2020
• 1991 AHSME Problems/Problem 22
  Two circles are externally tangent. Lines <math>\overline{PAB}</math> and <math>\overli ...PA'=A'B'=4</math>. We can then drop perpendiculars from the centers of the circles to the points of tangency and use similar triangles. Let us let the center
  2 KB (295 words) - 19:09, 11 October 2016
• 1990 AHSME Problems/Problem 6
  The lines have to be tangent to both of these circles.
  878 bytes (132 words) - 04:39, 4 February 2016
• 1969 AHSME Problems/Problem 6
  The area of the ring between two concentric circles is <math>12\tfrac{1}{2}\pi</math> square inches. The length of a chord of t
  1 KB (187 words) - 03:29, 7 June 2018
• 1969 AHSME Problems
  The area of the ring between two concentric circles is <math>12\tfrac{1}{2}\pi</math> square inches. The length of a chord of t
  16 KB (2,662 words) - 14:12, 20 February 2020
• 1987 AHSME Problems
  (Pretend the paper forms <math>600</math> concentric circles with diameters evenly spaced from <math>2</math> cm to <math>10</math> cm.)
  16 KB (2,291 words) - 13:45, 19 February 2020
• 1983 AHSME Problems
  In the adjoining figure the five circles are tangent to one another consecutively and to the lines
  15 KB (2,309 words) - 23:43, 2 December 2021
• 1982 AHSME Problems
  <math>O, N</math>, and <math>P</math>, respectively. Circles <math>O, N</math>, and <math>P</math> all have radius <math>15</math> and t
  17 KB (2,500 words) - 19:05, 11 September 2023
• 1979 AHSME Problems
  Circles with centers <math>A ,~ B</math>, and <math>C</math> each have radius <math
  17 KB (2,664 words) - 01:34, 19 March 2022
• 1977 AHSME Problems
  ...t to the other two, and each side of the triangle is tangent to two of the circles. If each circle has radius three, then the perimeter of the triangle is ...ath>, and let <math>P,Q,R</math>, and <math>S</math> be the centers of the circles
  15 KB (2,412 words) - 05:09, 27 November 2020
• 1976 AHSME Problems
  ...B) }\text{equal to the length of an external common tangent if and only if circles }\mathit{O}\text{ and }\mathit{O'} \text{have equal radii}\\
  17 KB (2,835 words) - 14:36, 8 September 2021
• 1969 IMO Problems/Problem 4
  ...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 ...math>c = AB</math>. Let <math>R, S, T</math> be the tangency points of the circles <math>K_1, K_2, K_3</math> with the line AB. In an inversion with the cente
  5 KB (904 words) - 13:42, 29 January 2021
• Mock AIME 5 2005-2006 Problems/Problem 7
  ...hin one of the smaller squares, it also lands completely within one of the circles. Let <math>P</math> be the probability that, when flipped onto the grid, th
  853 bytes (134 words) - 21:18, 8 October 2014
• 1971 AHSME Problems
  The ratio of the area of the first circle to the sum of areas of all other circles in the sequence, is
  18 KB (2,703 words) - 20:50, 11 September 2023
• 2013 UNCO Math Contest II Problems
  In the diagram, the two circles are tangent to the two parallel lines. The distance between the centers of the circles is 8, and both circles have
  11 KB (1,648 words) - 09:55, 20 December 2021
• 2013 UNCO Math Contest II Problems/Problem 1
  In the diagram, the two circles are tangent to the two parallel lines. The distance between the centers of the circles is <math>8</math>, and both circles have
  1 KB (162 words) - 14:13, 24 February 2022
• 2012 UNCO Math Contest II Problems
  and both circles are tangent to a line. Find the area of the shaded region that lies between the two circles and the line.
  6 KB (1,018 words) - 15:05, 20 August 2020

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