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• 2012 UNCO Math Contest II Problems/Problem 7
  and both circles are tangent to a line. Find the area of the shaded region that lies between the two circles and the line.
  2 KB (336 words) - 12:57, 2 January 2020
• 2007 UNCO Math Contest II Problems
  forever what is the total area of all the circles? Express
  6 KB (890 words) - 22:14, 7 November 2014
• 2007 UNCO Math Contest II Problems/Problem 9
  forever what is the total area of all the circles? Express ...let <math>A_1B_1</math> be the internal common tangent of the two largest circles, with the points <math>A_1</math> and <math>B_1</math> laying on the sides
  3 KB (412 words) - 18:49, 29 January 2018
• 1987 AHSME Problems/Problem 13
  (Pretend the paper forms <math>600</math> concentric circles with diameters evenly spaced from <math>2</math> cm to <math>10</math> cm.) ...h of the paper is equal to the sum of the circumferences of the concentric circles, which is <math>\pi</math> times the sum of the diameters. Now the, the dia
  1 KB (199 words) - 14:24, 1 March 2018
• 2016 AMC 12A Problems
  ...with center <math>Q</math> is externally tangent to each of the other two circles. What is the area of triangle <math>PQR</math>?
  15 KB (2,348 words) - 17:20, 19 January 2024
• 2014 UNM-PNM Statewide High School Mathematics Contest II Problems
  Find the smallest and largest possible distances between the centers of two circles of radius the circles and the third vertex on the second circle.
  5 KB (774 words) - 06:07, 29 January 2019
• 2014 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 4
  Find the smallest and largest possible distances between the centers of two circles of radius the circles and the third vertex on the second circle.
  2 KB (315 words) - 22:44, 17 November 2019
• 2014 AMC 8 Problems
  ...osest to the area of the region inside the rectangle but outside all three circles?
  13 KB (1,957 words) - 12:08, 13 January 2024
• 2014 AMC 8 Problems/Problem 25
  ...frac{5280}{40} =132</math> semicircles in total. Were the semicircles full circles, their circumference would be <math>2\pi\cdot 20=40\pi</math> feet; as it i
  2 KB (395 words) - 12:16, 17 January 2024
• 2014 AMC 8 Problems/Problem 20
  ...osest to the area of the region inside the rectangle but outside all three circles? ...es is the area of the rectangle minus the area of all three of the quarter circles in the rectangle.
  2 KB (249 words) - 20:36, 2 January 2023
• 2015 UNCO Math Contest II Problems
  ...er circle has radius <math>3</math>. The shaded region is outlined by half circles whose radii are <math>1</math> and <math>2</math> and whose centers lie on
  7 KB (1,151 words) - 15:11, 20 August 2020
• 2015 UNCO Math Contest II Problems/Problem 2
  ...er circle has radius <math>3</math>. The shaded region is outlined by half circles whose radii are <math>1</math> and <math>2</math> and whose centers lie on
  1 KB (154 words) - 09:47, 6 March 2024
• 2015 AMC 12A Problems
  ...dius <math>3</math>, and all possible lines simultaneously tangent to both circles. Isabella notices that she has drawn exactly <math>k \ge 0</math> lines. Ho ...s in the pair. Layer <math>L_k</math> consists of the <math>2^{k-1}</math> circles constructed in this way. Let <math>S=\bigcup_{j=0}^{6}L_j</math>, and for e
  13 KB (2,117 words) - 12:33, 24 August 2023
• 2015 AMC 12A Problems/Problem 11
  ...dius <math>3</math>, and all possible lines simultaneously tangent to both circles. Isabella notices that she has drawn exactly <math>k \ge 0</math> lines. H Isabella can get <math>0</math> lines if the circles are concentric, <math>1</math> if internally tangent, <math>2</math> if ove
  823 bytes (123 words) - 13:24, 29 March 2015
• 2015 AMC 12A Problems/Problem 23
  ...us (like there always is) that I think was mentioned above, something with circles (since the thing under the square root is just <math>x^2+y^2 = \frac{1}{4}<
  12 KB (1,981 words) - 18:33, 3 September 2023
• 2015 AMC 12A Problems/Problem 25
  ...s in the pair. Layer <math>L_k</math> consists of the <math>2^{k-1}</math> circles constructed in this way. Let <math>S=\bigcup_{j=0}^{6}L_j</math>, and for e // draw the big circles and the bottom line
  8 KB (1,340 words) - 14:24, 23 November 2023
• 2015 AMC 12B Problems
  ...ath>D</math>, and points <math>P</math> and <math>Q</math> lie on all four circles. The radius of circle <math>A</math> is <math>\tfrac{5}{8}</math> times the
  13 KB (2,064 words) - 13:39, 1 October 2022
• 2015 AMC 12B Problems/Problem 19
  ...n of the shapes inside the triangle, so we think of things associated with circles and think of cyclic quads. We then notice that quadrilateral <math>WXYZ</ma
  11 KB (1,898 words) - 22:42, 16 June 2023
• 2015 AMC 12B Problems/Problem 24
  ...ath>D</math>, and points <math>P</math> and <math>Q</math> lie on all four circles. The radius of circle <math>A</math> is <math>\tfrac{5}{8}</math> times the ...Suppose that <math>O_1</math> and <math>O_2</math> are the centers of two circles <math>C_1</math> and <math>C_2</math> that intersect exactly at <math>P</ma
  7 KB (1,188 words) - 19:18, 19 October 2023
• 2015 AIME I Problems/Problem 15
  ...D (from the top perspective) is 10:6. Using 30-60-90 triangles and partial circles, the area of the base between AB and CD is calculated to be <math>18\sqrt{3
  9 KB (1,407 words) - 19:37, 17 February 2024

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