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• 2019 AIME II Problems/Problem 7
  ...iangle ABC</math>, so using similar triangle ratios, we find that <math>BI=HA=30</math>, <math>BD=HG=55</math>, <math>FC=\frac{45}{2}</math>, and <math>E
  7 KB (1,053 words) - 14:58, 14 January 2024
• 2019 AIME I Problems/Problem 11
  ...\cdot \frac{h+r_{I_A}}{h-r} = \frac{hb}{a+b} \cdot \frac{h+r_{I_A}}{\frac{ha}{a+b}} = \frac{b(h+r_{I_A})}{a}</math>. Now, solving yields <math>r_{I_A} = <math> \implies 3ha + h + ha^2 - h = \sqrt{2a^2 + 2a} \cdot a(a-1)</math>
  21 KB (3,915 words) - 19:55, 10 October 2023
• 2020 AIME I Problems/Problem 15
  ...<math>\omega</math> at points <math>X</math> and <math>Y</math> with <math>HA=3,HX=2,</math> and <math>HY=6.</math> The area of <math>\triangle ABC</math .../math>. The Power of a Point Theorem yields <math>HP = \tfrac{HX \cdot HY}{HA} = 4</math>. Because <math>\angle CAP=\angle CBP</math>, and <math>\angle C
  16 KB (2,678 words) - 22:45, 27 November 2023
• 2019 AMC 8 Problems/Problem 9
  ..., with ra being Alex's radius<math> (1/2 \cdot</math> diameter), and <math>ha</math> being her cylinders height<math> ...ed the ratio between Alexa's and Felicias, we can do <math>(\pi ra^2)\cdot ha/(\pi rf^2)\cdot hf</math> The <math>\pi</math> cancel out, then substitute
  3 KB (489 words) - 16:37, 30 December 2023
• 2020 AMC 10B Problems/Problem 21
  ...h> is a right isosceles triangle with area 1, we can determine sides <math>HA</math> and <math>AE</math> both to be <math>\sqrt{2}</math>. Now, consider
  11 KB (1,850 words) - 23:33, 27 March 2024
• 2020 AIME I Problems
  ...<math>\omega</math> at points <math>X</math> and <math>Y</math> with <math>HA=3,HX=2,</math> and <math>HY=6.</math> The area of <math>\triangle ABC</math
  7 KB (1,257 words) - 17:51, 5 February 2022
• 2021 CIME I Problems/Problem 14
  ...le ABC\cup A'</math>, so <cmath>\frac{AD}{2R}=1-\frac{A'D}{2R}=1-\frac{HS}{HA}=1-\cos A,</cmath> i.e.\ <math>AD=2R(1-\cos A)</math>. We are given <math>R
  3 KB (538 words) - 14:38, 26 January 2021
• 2021 April MIMC 10
  ...math> (formed by side <math>AB</math>, arc <math>BH</math>, and side <math>HA</math>), <math>DFE</math> (formed by side <math>ED</math>, arc <math>DF</ma ...<math>DE</math>, <math>EF</math>, <math>FG</math>, <math>GH</math>, <math>HA</math>.
  15 KB (2,366 words) - 17:45, 19 September 2021
• 2021 Fall MIMC 10
  ...math> (formed by side <math>AB</math>, arc <math>BH</math>, and side <math>HA</math>), <math>DFE</math> (formed by side <math>ED</math>, arc <math>DF</ma ...<math>DE</math>, <math>EF</math>, <math>FG</math>, <math>GH</math>, <math>HA</math>.
  14 KB (2,226 words) - 23:39, 12 September 2021
• 2021 April MIMC 10 Problems/Problem 23
  ...math> (formed by side <math>AB</math>, arc <math>BH</math>, and side <math>HA</math>), <math>DFE</math> (formed by side <math>ED</math>, arc <math>DF</ma ...math> (formed by side <math>AB</math>, arc <math>BH</math>, and side <math>HA</math>), <math>DFE</math> (formed by side <math>ED</math>, arc <math>DF</ma
  3 KB (520 words) - 14:04, 26 April 2021
• 2021 April MIMC 10 Problems/Problem 24
  ...<math>DE</math>, <math>EF</math>, <math>FG</math>, <math>GH</math>, <math>HA</math>.
  3 KB (599 words) - 14:05, 26 April 2021

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