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

• 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
• 1998 AHSME Problems/Problem 11
  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
  929 bytes (132 words) - 14:29, 5 July 2013
• 1985 AJHSME Problems/Problem 24
  ...number|whole numbers]] <math>10-15</math> is placed in one of the [[circle|circles]] so that the sum, <math>S</math>, of the three numbers on each side of the
  2 KB (207 words) - 10:05, 10 June 2024
• 1986 AJHSME Problems
  ...the ratio of the area of the shaded region to the area of one of the small circles?
  14 KB (2,054 words) - 15:41, 8 August 2020
• 1986 AJHSME Problems/Problem 23
  ...the ratio of the area of the shaded region to the area of one of the small circles?
  2 KB (277 words) - 21:32, 3 July 2013
• 2004 AMC 10B Problems/Problem 16
  Three circles of radius <math>1</math> are externally tangent to each other and internall ...1}{r}</math> (b/c the bigger circle is externally tangent to all the other circles, the radius of the bigger circle is negative). Then, we can solve:
  2 KB (287 words) - 14:05, 5 January 2022
• 2004 AMC 10B Problems/Problem 22
  ...a circumscribed circle. What is the distance between the centers of those circles?
  5 KB (700 words) - 13:46, 6 April 2024
• 2004 AMC 10B Problems/Problem 25
  ...ture, that is outside the smaller circle and inside each of the two larger circles? Let <math>C</math> and <math>D</math> be the intersections of the two large circles. Connect them to <math>A</math> and <math>B</math> to get the picture below
  4 KB (715 words) - 18:24, 26 June 2024
• 2004 AMC 12B Problems/Problem 10
  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<
  2 KB (340 words) - 14:35, 23 April 2023
• 2009 AMC 12A Problems
  ...around the pentagon, and calculated the area of the region between the two circles. Bethany did the same with a regular heptagon (7 sides). The areas of the
  13 KB (2,105 words) - 13:13, 12 August 2020
• 2009 AMC 10A Problems
  ...s it rolls once around the circumference of circle <math>A</math>. The two circles have the same points of tangency at the beginning and end of circle <math>B ...les is four. What is the ratio of the sum of the areas of the four smaller circles to the area of the larger circle?
  14 KB (2,126 words) - 17:46, 13 June 2024
• 2009 AMC 12A Problems/Problem 19
  ...around the pentagon, and calculated the area of the region between the two circles. Bethany did the same with a regular heptagon (7 sides). The areas of the ...itude we dropped to the side of each polygon) are the radii of the smaller circles.
  4 KB (630 words) - 21:27, 30 December 2023
• 2009 AMC 10A Problems/Problem 18
  ...e total number of students be <math>100</math>. Draw a venn diagram with 2 circles encompassing these 4 regions:
  3 KB (402 words) - 10:29, 2 August 2021
• 2009 AMC 10A Problems/Problem 21
  ...les is four. What is the ratio of the sum of the areas of the four smaller circles to the area of the larger circle? Draw some of the radii of the small circles as in the picture below.
  3 KB (474 words) - 12:50, 29 September 2023
• 2009 AMC 10A Problems/Problem 19
  ...s it rolls once around the circumference of circle <math>A</math>. The two circles have the same points of tangency at the beginning and end of circle <math>B
  2 KB (276 words) - 09:57, 8 June 2021
• 2001 AMC 12 Problems/Problem 18
  ...>\overline{AC}</math>. Moreover, the small circle is tangent to both other circles, hence we have <math>SA=1+r</math> and <math>SB=4+r</math>. ...e: This case corresponds to the other circle that is tangent to both given circles and the common tangent line. By coincidence, due to the <math>4:1</math> ra
  5 KB (822 words) - 01:35, 7 February 2024
• 2002 AMC 12A Problems/Problem 5
  ...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 ...s radius <math>1+1+1=3</math>, and thus area <math>9\pi</math>. The little circles have area <math>\pi</math> each; since there are 7, their total area is <ma
  1 KB (192 words) - 12:35, 8 November 2021
• 2009 AMC 10A Problems/Problem 6
  ...hat is inscribed in it. Double means that <math>2</math> of the small full circles will be able to fit the larger semi-circle. So, therefore, the area that is
  2 KB (380 words) - 09:21, 8 June 2021
• 2002 AMC 12A Problems/Problem 18
  Let <math>C_1</math> and <math>C_2</math> be circles defined by <math>(x-10)^2 + y^2 = 36</math> and <math>(x+15)^2 + y^2 = 81</ Line PQ is tangent to both circles, so it forms a right angle with the radii (6 and 9). This, as well as the t
  3 KB (485 words) - 03:13, 1 September 2023
• 2009 AIME II Problems
  ...gent to circle <math>A</math> at the other two vertices of <math>T</math>. Circles <math>B</math>, <math>C</math>, and <math>D</math> are all externally tange
  8 KB (1,366 words) - 13:59, 24 June 2024

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