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- 0 bytes (0 words) - 12:26, 6 February 2024
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- In these proofs, we will let <math>ABC </math> be any right triangle with a right angle at <math>\angle ACB</math> We use <math>[ABC] </math> to denote the area of triangle <math>ABC </math>.5 KB (885 words) - 22:03, 5 October 2024
- ...formations will return <math>\triangle A''B''C''</math> to <math>\triangle ABC</math>?1 KB (235 words) - 13:52, 25 June 2023
- ...(a+1)(b+1)(c+1) = 8</math>, and <math>a, b, c \ge 0</math> show that <math>abc \le 1</math>. (<url>weblog_entry.php?t=172070 Source</url>)12 KB (1,806 words) - 05:07, 19 June 2024
- ...ath>B</math>, and <math>C</math> are points of tangency, that circle <math>ABC</math> is inscribed in <math>\triangle DEF</math>. The height of an equilat3 KB (415 words) - 17:01, 24 May 2020
- Let <math>ABC</math> be an acute triangle with <math>AB > AC</math>. Let <math>\Gamma</ma Triangle <math>ABC</math> has circumcircle <math>\Omega</math> and circumcenter <math>O</math>4 KB (709 words) - 14:00, 1 June 2024
- *Triangle <math>ABC</math> has <math>AB=9</math> and <math>BC: AC=40: 41</math>. What is the la3 KB (583 words) - 20:20, 2 August 2024
- <cmath>[ABC]=\frac{ab}{2}\sin C, </cmath> <cmath>[ABC]=\frac{ab}{2}\sqrt{1-\cos^2 C}.</cmath>4 KB (675 words) - 22:45, 6 October 2024
- *<math>(a+b+c)^7=a^7+b^7+c^7+7(a+b)(b+c)(c+a)((a^2+b^2+c^2+ab+bc+ca)^2+abc(a+b+c))</math> * Given that <math>a+b+c=0</math>, prove that <math>abc=\dfrac{a^3+b^3+c^3}{3}</math>.3 KB (532 words) - 21:00, 13 January 2024
- ...ter with combinations, there is only one combination of those three.(<math>ABC,ACB,BAC,BCA,CAB,CBA</math> are all equivalent in combination but different .../math>) but in combinations the order of arrangement does not matter(<math>ABC</math> is equivalent to <math>ACB</math>).For its derivation see this [http4 KB (615 words) - 10:43, 21 May 2021
- Case I) <math>a+b=c\Rightarrow c+c^2=abc\Rightarrow 1+c=ab\Rightarrow1+a+b=ab\Rightarrow (a-1)(b-1)=2</math>2 KB (332 words) - 08:37, 30 December 2021
- *Let <math>ABC</math> be a triangle such that ...semiperimeter]] and [[inradius]], respectively. Prove that triangle <math>ABC </math> is similar to a triangle <math>T </math> whose side lengths are all13 KB (2,048 words) - 14:28, 22 February 2024
- If line <math>PQ</math> intersecting <math>AB</math> on <math>\triangle ABC</math>, where <math>P</math> is on <math>BC</math>, <math>Q</math> is on th5 KB (804 words) - 02:01, 12 June 2023
- Find the area of the largest triangle <math>ABC</math> [and prove this is the maximum] whose interior is entirely within th3 KB (551 words) - 15:22, 13 September 2023
- *In <math>\triangle ABC</math>, <math>\sin{A}+\sin{B}+\sin{C}\le \frac{3\sqrt{3}}{2}</math>. Similarly, in <math>\triangle ABC</math>, <math>\cos{A}+\cos{B}+\cos{C}\le \frac{3}{2}</math>.7 KB (1,300 words) - 00:11, 28 October 2024
- ...ADC,</math> so <math>\angle ADP=\angle ABC</math>. Hence, <math>\triangle ABC \sim \triangle ADP</math> by AA similarity and <math>\frac{AB}{AD}=\frac{BC In triangle <math>ABC</math> we have <math>AB=7</math>, <math>AC=8</math>, <math>BC=9</math>. Poi7 KB (1,198 words) - 08:36, 8 December 2024
- 3rd Symmetric Sum = <math>S_3 = abc+abd+acd+bcd</math>2 KB (275 words) - 11:51, 26 July 2023
- ...the [[incenter]] and [[excenter]] of a triangle. Given any <math>\triangle ABC</math> with incenter <math>I</math> and <math>A</math>-excenter <math>I_A</2 KB (291 words) - 15:31, 18 May 2021
- [[Image:Acute_orthic_triangle.png|thumb|right|300px|Case 1: <math>\triangle ABC</math> is acute.]] [[Image:Obtuse_orthic_triangle.png|thumb|right|300px|Case 2: <math>\triangle ABC</math> is obtuse.]]8 KB (1,408 words) - 08:39, 10 July 2024
- * Prove that for any <math>\triangle ABC</math>, we have <math>\sin{A}+\sin{B}+\sin{C}\leq \frac{3\sqrt{3}}{2}</math * Show that in any triangle <math>\triangle ABC</math> we have <math>\cos {A} \cos{B} \cos {C} \leq \frac{1}{8}</math>3 KB (628 words) - 05:29, 28 November 2024
- In the following figure, <math>AM</math> is a median of triangle <math>ABC</math>. ...h>. This occurs when <math>M</math> is the circumcenter of <math>\triangle ABC.</math>1 KB (185 words) - 19:24, 6 March 2024