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• Pythagorean Theorem
  <math> \frac{[ABC]}{AB^2} = \frac{[CBH]}{CB^2} = \frac{[ACH]}{AC^2} </math>. ...h>ACH </math>, <math>[ABC] = [CBH] + [ACH] </math>, so <math>AB^2 = CB^2 + AC^2 </math>. {{Halmos}}
  5 KB (886 words) - 13:51, 15 May 2024
• Law of Sines
  <cmath>\frac{1}{2}bc\sin A = \frac{1}{2}ac\sin B = \frac{1}{2}ab\sin C </cmath> ...<math>\overline{AC}</math> that is not on the same side of <math>\overline{AC}</math> as <math>B</math>. The length of <math>\overline{AD}</math> can be
  4 KB (658 words) - 16:19, 28 April 2024
• Homothety
  ...<math>\omega_{A}</math> is [[tangent]] to sides <math>AB</math> and <math>AC</math>, <math>\omega_{B}</math> to <math>BC</math> and <math>BA</math>, <ma ([[2007 AIME II Problems/Problem 15|Source]])
  3 KB (532 words) - 01:11, 11 January 2021
• 2006 AMC 12B Problems
  ...=11</math>, <math>PB=7</math>, and <math>PC=6</math>. Legs <math>\overline{AC}</math> and <math>\overline{BC}</math> have length <math>s=\sqrt{a+b\sqrt{2 {{AMC12 box|year=2006|ab=B|before=[[2006 AMC 12A Problems]]|after=[[2007 AMC 12A Problems]]}}
  13 KB (2,058 words) - 12:36, 4 July 2023
• Inradius
  ...{AI}, \overline{BI}</math>, and <math>\overline{CI}</math>. After this AB, AC, and BC are the bases of <math>\triangle{AIB}, {AIC}</math>, and <math>{BIC *[[2007 AIME II Problems/Problem 15]]
  2 KB (321 words) - 22:54, 20 June 2024
• Mock AIME 1 2006-2007 Problems/Problem 1
  ...th>\angle BAD = \angle CAD</math> so <math>\frac{[ABD]}{[ACD]} = \frac{AB}{AC}</math>. *[[Mock AIME 1 2006-2007 Problems/Problem 2 | Next Problem]]
  2 KB (329 words) - 15:53, 3 April 2012
• Mock AIME 1 2006-2007 Problems/Problem 7
  Let <math>\triangle ABC</math> have <math>AC=6</math> and <math>BC=3</math>. Point <math>E</math> is such that <math>CE= ...A]=\frac{CF}{CB}\cdot [ABC]=\frac{2x}{3}</math>, and <math>[AEF]=\frac{AE}{AC}\cdot [CFA]=\frac{5}{6}\cdot \frac{2x}{3}=\frac{5x}{9}</math>. Similarly, <
  3 KB (518 words) - 16:54, 25 November 2015
• Mock AIME 1 2006-2007/Problems
  [[Mock AIME 1 2006-2007 Problems/Problem 1|Solution]] [[Mock AIME 1 2006-2007 Problems/Problem 2|Solution]]
  8 KB (1,355 words) - 14:54, 21 August 2020
• Mock AIME 2 2006-2007 Problems/Problem 9
  ...th> intersect at <math>P</math> and are drawn to <math>BC</math> and <math>AC</math> respectively such that <math>\frac{BX}{CX}=\frac23</math>, <math>\fr ...nd <math>E</math> be the projections of <math>P</math> onto the legs <math>AC</math> and <math>BC</math> respectively. Remark that <math>\tan\angle DPB=
  2 KB (358 words) - 23:22, 3 May 2014
• Mock AIME 2 2006-2007 Problems/Problem 14
  In [[triangle]] <math>ABC</math>, <math>AB = 308</math> and <math>AC=35</math>. Given that <math>AD</math>, <math>BE,</math> and <math>CF,</mat [[Image:Mock AIME 2 2007 Problem14.jpg]]
  2 KB (284 words) - 10:53, 4 April 2012
• Mock AIME 2 2006-2007 Problems
  [[Mock_AIME_2_2006-2007 Problems/Problem_1|Solution]] The set <math>S</math> consists of all integers from <math>1</math> to <math>2007,</math> inclusive. For how many elements <math>n</math> in <math>S</math> i
  5 KB (848 words) - 23:49, 25 February 2017
• 2007 iTest Problems
  [[2007 iTest Problems/Problem 1|Solution]] <math>3a + 7b = 1977</math> and <math>5a + b = 2007</math>.
  30 KB (4,794 words) - 23:00, 8 May 2024
• Mock AIME 4 2006-2007 Problems/Problem 11
  ...math>E</math> are chosen on <math>\overline{AB}</math> and <math>\overline{AC}</math>, respectively, such that <math>AD = CE</math>. Let <math>F</math> b *[[Mock AIME 4 2006-2007 Problems/Problem 12| Next Problem]]
  2 KB (325 words) - 19:33, 9 February 2017
• Mock AIME 4 2006-2007 Problems/Problem 15
  ...<math>\overline{AC}</math> that is not on the same side of <math>\overline{AC}</math> as <math>B</math>. The length of <math>\overline{AD}</math> can be ...of that circle. Let <math>M</math> be the [[midpoint]] of <math>\overline{AC}</math>, and <math>R</math> be the length of the [[radius]] of <math>\omega
  3 KB (532 words) - 20:29, 31 August 2020
• 2007 AIME I Problems
  {{AIME Problems|year=2007|n=I}} [[2007 AIME I Problems/Problem 1|Solution]]
  7 KB (1,218 words) - 15:28, 11 July 2022
• 2007 AIME I Problems/Problem 10
  [[Image:AIME I 2007-10.png]] [[Image:AIME I 2007-10b.PNG|thumbnail|left|200px|One example of each case for the first two col
  13 KB (2,328 words) - 00:12, 29 November 2023
• 2007 AIME I Problems/Problem 9
  [[Image:AIME I 2007-9.png]] [[Image:AIME I 2007-9b.png|left]]
  11 KB (1,851 words) - 12:31, 21 December 2021
• 2007 AIME I Problems/Problem 12
  ...h>(20,0)</math>. Point <math>C</math> is in the first quadrant with <math>AC = BC</math> and angle <math>BAC = 75^{\circ}</math>. If triangle <math>ABC ...riangles). Let <math>\overline{B'C'}</math> intersect with <math>\overline{AC}</math> at point <math>D</math>, <math>\overline{BC}</math> intersect with
  10 KB (1,458 words) - 20:50, 3 November 2023
• 2007 AIME II Problems/Problem 15
  ...<math>\omega_{A}</math> is [[tangent]] to sides <math>AB</math> and <math>AC</math>, <math>\omega_{B}</math> to <math>BC</math> and <math>BA</math>, <ma [[Image:2007 AIME II-15b.gif]]
  11 KB (2,099 words) - 17:51, 4 January 2024
• 2007 AIME II Problems
  {{AIME Problems|year=2007|n=II}} ...than it appears among the four letters in AIME or the four digits in <math>2007</math>. A set of plates in which each possible sequence appears exactly onc
  9 KB (1,435 words) - 01:45, 6 December 2021

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