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Page title matches

• Math circles
  ...around North America. Inspired by Eastern European teaching models, math circles often take a problem-discussion approach to teaching and learning [[mathema == Math Circles by City ==
  3 KB (436 words) - 18:35, 26 August 2021
• What is the greatest number of points of intersection that can occur when $2$ different circles and $2$ different straight lines are drawn on the same piece of paper?
  ...ber of points of intersection that can occur when <math>2</math> different circles and <math>2</math> different straight lines are drawn on the same piece of ...rcles in <math>4</math> points. Draw another line which intersects the two circles in <math>4</math> points and also intersects the first line. There are <mat
  1 KB (188 words) - 17:11, 7 August 2020
• PaperMath’s circles
  ==PaperMath’s circles== ...of the congruent circles and where <math>n</math> is the number of tangent circles.
  4 KB (665 words) - 23:04, 27 March 2024

Page text matches

• 2005 AMC 12A Problems/Problem 16
  ...ius <math>r > s</math> is tangent to both axes and to the second and third circles. What is <math>r/s</math>?
  2 KB (307 words) - 15:30, 30 March 2024
• California mathematics competitions
  * [[Math circles]] -- There are many in California.
  4 KB (514 words) - 04:02, 21 September 2023
• Mathematics websites
  * [http://www.geometer.org/mathcircles/ Tom Davis's] site for [[math circles]] topics. * [http://www.geometer.org/mathcircles/ Tom Davis's] site for [[math circles]] topics.
  4 KB (516 words) - 03:01, 13 April 2023
• Math books
  ...//www.amazon.com/exec/obidos/ASIN/0821804308/artofproblems-20 Mathematical Circles] -- A wonderful peak into Russian math training.
  24 KB (3,177 words) - 12:53, 20 February 2024
• Math circles
  ...around North America. Inspired by Eastern European teaching models, math circles often take a problem-discussion approach to teaching and learning [[mathema == Math Circles by City ==
  3 KB (436 words) - 18:35, 26 August 2021
• San Diego Math Circle
  * [[Math circles]]
  713 bytes (94 words) - 13:36, 10 June 2008
• ARML historical results
  |[[Toronto Math Circles]] (Toronto Math Circles B1)
  19 KB (2,632 words) - 14:31, 12 June 2022
• Circle
  ==Lines in Circles== *How many circles with radius <math>r</math> can we fit around a circle with radius <math>r</
  9 KB (1,581 words) - 18:59, 9 May 2024
• Ellipse
  *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
  5 KB (892 words) - 21:52, 1 May 2021
• Planar figure
  327 bytes (41 words) - 22:27, 24 April 2008
• Homothety
  ...n use properties of similarity. Additionally, similarity (especially with circles) where parallel lines are used can indicate that homothety can be used, and
  3 KB (532 words) - 01:11, 11 January 2021
• Area
  6 KB (1,181 words) - 22:37, 22 January 2023
• 2006 AIME I Problems
  Eight circles of diameter 1 are packed in the first quadrant of the coordinate plane as s
  7 KB (1,173 words) - 03:31, 4 January 2023
• 2006 AIME I Problems/Problem 10
  ...ed circles splitting into congruent areas, and there are an additional two circles on each side. The line passes through <math>\left(1,\frac 12\right)</math> Assume that if unit [[square]]s are drawn circumscribing the circles, then the line will divide the area of the [[concave]] hexagonal region of
  4 KB (731 words) - 17:59, 4 January 2022
• 2021 JMC 10
  ...ers that are <math>\tfrac{4}{3}</math> units apart. Two externally tangent circles <math>\omega_1</math> and <math>\omega_2</math> of radius <math>r_1</math>
  12 KB (1,784 words) - 16:49, 1 April 2021
• 2006 AMC 12B Problems
  .../math> and <math> \overline{BC}</math> are common external tangents to the circles. What is the area of hexagon <math> AOBCPD</math>?
  13 KB (2,058 words) - 12:36, 4 July 2023
• 2006 AMC 12A Problems
  ...nally tangent circles, as shown. What is the sum of the areas of the three circles? ...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
  15 KB (2,223 words) - 13:43, 28 December 2020
• 2005 AMC 12A Problems
  ...ius <math>r > s</math> is tangent to both axes and to the second and third circles. What is <math>r/s</math>?
  13 KB (1,971 words) - 13:03, 19 February 2020
• 2004 AMC 12A Problems
  ...ly tangent to each other, and internally tangent to circle <math>D</math>. Circles <math>B</math> and <math>C</math> are congruent. Circle <math>A</math> has
  13 KB (1,953 words) - 00:31, 26 January 2023
• 2002 AMC 12A Problems
  ...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 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</
  12 KB (1,792 words) - 13:06, 19 February 2020
• 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
• 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) - 12:53, 6 July 2022
• 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

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