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Page title matches

• Obtuse triangle
  ...in which one [[angle]] is an [[obtuse angle]]. Any triangle which is not obtuse is either a [[right triangle]] or an [[acute triangle]]. ...e because the angles of a triangle must sum to <math>180^\circ</math>. Two obtuse angles would sum to more than that.
  1 KB (193 words) - 14:20, 12 June 2022
• Obtuse angle
  An '''obtuse angle''' is an [[angle]] with a [[measure]] greater than 90 [[degree (geome Any triangle with an obtuse angle is considered an [[Obtuse Triangle]]
  508 bytes (62 words) - 17:21, 2 March 2014
• Obtuse Triangle
  #REDIRECT [[Obtuse triangle]]
  29 bytes (3 words) - 17:22, 2 March 2014
• Obtuse triangles
  ...triangle that has one angle that is greater than 90, which is called and [[Obtuse Angle]].
  100 bytes (18 words) - 14:30, 7 January 2022
• Obtuse Angle
  An Obtuse angle is a angle greater than 90.
  43 bytes (8 words) - 14:31, 7 January 2022

Page text matches

• Geometric inequality
  ...a^2 + b^2 = c^2</math>. The Inequality extends this to [[obtuse triangle| obtuse]] and [[acute triangle]]s. The inequality says: ...s of length <math>a \leq b \leq c</math>, <math>a^2+b^2>c^2</math>. For an obtuse triangle with sides <math>a \leq b \leq c</math>, <math>a^2+b^2<c^2</math>.
  7 KB (1,296 words) - 14:22, 22 October 2023
• Orthic triangle
  ...rthic_triangle.png|thumb|right|300px|Case 2: <math>\triangle ABC</math> is obtuse.]] ...right. The two cases of when <math>\triangle ABC</math> is either acute or obtuse each carry different characteristics and must be handled separately.
  8 KB (1,408 words) - 11:54, 8 December 2021
• Triangle
  ===Obtuse=== ...n equilateral obtuse triangle. It is also impossible to have more than one obtuse angle in a triangle.
  4 KB (628 words) - 17:17, 17 May 2018
• Law of Cosines
  ===Obtuse Triangle=== The argument for an obtuse triangle is the same as the proof for an acute triangle.
  6 KB (1,003 words) - 09:11, 7 June 2023
• Trigonometry
  ...ing right triangles, trigonometry is just as useful when used on acute and obtuse triangles. The [[Law of Sines]] and [[Law of Cosines]] mentioned below gene
  8 KB (1,217 words) - 20:15, 7 September 2023
• Right triangle
  *[[Obtuse triangle]]
  3 KB (499 words) - 23:41, 11 June 2022
• 2021 JMC 10
  ...termine two angles of a triangle. What is the probability this triangle is obtuse?
  12 KB (1,784 words) - 16:49, 1 April 2021
• 2001 AMC 12 Problems
  ...th>E=(0,4)</math>. What is the probability that <math>\angle APB</math> is obtuse?
  13 KB (1,957 words) - 12:53, 24 January 2024
• 2006 AMC 12B Problems/Problem 23
  ...le BPA</math>, <math>\angle APC</math> and <math>\angle BPC</math> must be obtuse, since they sum to <math>360^{\circ}</math>. Then, note the well known fact
  7 KB (1,169 words) - 14:04, 10 June 2022
• Right angle
  ** [[Obtuse angle]]
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• Acute triangle
  ...]. Any triangle which is not acute is either a [[right triangle]] or an [[obtuse triangle]]. ...so can be scalene. There are Acute [[triangle]],[[Right triangles]], and [[Obtuse triangles]].
  1 KB (194 words) - 13:09, 20 February 2024
• Obtuse triangle
  ...in which one [[angle]] is an [[obtuse angle]]. Any triangle which is not obtuse is either a [[right triangle]] or an [[acute triangle]]. ...e because the angles of a triangle must sum to <math>180^\circ</math>. Two obtuse angles would sum to more than that.
  1 KB (193 words) - 14:20, 12 June 2022
• Orthocenter
  ...on the vertex opposite the [[hypotenuse]]; and if it is [[obtuse triangle|obtuse]], then the orthocenter is outside the triangle.
  5 KB (829 words) - 13:11, 20 February 2024
• 1970 Canadian MO Problems
  Given a triangle <math>ABC</math> with angle <math>A</math> obtuse and with altitudes of length <math>h</math> and <math>k</math> as shown in
  4 KB (604 words) - 04:32, 8 October 2014
• Angle
  ...le but less than that of a straight angle, i.e. <math>\angle ABC</math> is obtuse if and only if <math>90^\circ<m\angle ABC<180^\circ</math>.
  3 KB (568 words) - 20:21, 21 June 2019
• Straight angle
  ** [[Obtuse angle]]
  568 bytes (78 words) - 13:50, 12 June 2022
• Obtuse angle
  An '''obtuse angle''' is an [[angle]] with a [[measure]] greater than 90 [[degree (geome Any triangle with an obtuse angle is considered an [[Obtuse Triangle]]
  508 bytes (62 words) - 17:21, 2 March 2014
• Euler line
  <i><b>Obtuse triangle</b></i> [[File:Euler line obtuse triangle.png|400px|right]]
  59 KB (10,203 words) - 04:47, 30 August 2023
• Mock AIME 4 2006-2007 Problems/Problem 15
  ...ake the positive sign because [[angle]] <math>B</math> is [[obtuse angle | obtuse]] so <math>\overline{MD}</math> is the longer of the two [[line segment | s
  3 KB (532 words) - 20:29, 31 August 2020
• 2002 USAMO Problems/Problem 2
  Sidenote: A 13, 40, 45 obtuse triangle has an integer area of 252 and an inradius of <math>\frac{36}{7}</
  2 KB (298 words) - 22:32, 6 April 2016
• 2002 USA TST Problems/Problem 1
  ...positely sorted. But if one angle, say <math> \displaystyle A </math>, is obtuse, then we must have <math> \sin B, \sin C \le \sin (B+C) = \sin A </math>, a
  2 KB (380 words) - 20:16, 3 April 2007
• Reflex angle
  ** [[Obtuse angle]]
  1 KB (153 words) - 19:32, 31 December 2019
• De Longchamps point
  De Longchamps circle <math>\Omega</math> of the obtuse triangle <math>ABC</math> is circle centered at de Longchamps point <math>L Let <math>ABC</math> be obtuse triangle <math>(\angle A > 90^\circ)</math> with circumcircle <math>\Omega,
  10 KB (1,780 words) - 09:23, 17 November 2022
• 1995 AHSME Problems
  ...math> is an integer. For how many values of <math>k</math> is the triangle obtuse?
  17 KB (2,387 words) - 22:44, 26 May 2021
• 1995 AHSME Problems/Problem 23
  ...math> is an integer. For how many values of <math>k</math> is the triangle obtuse? By the [[Law of Cosines]], a triangle is obtuse if the sum of the squares of two of the sides of the triangles is less than
  1 KB (183 words) - 14:05, 5 July 2013
• Euclid's Elements
  *An obtuse angle is an angle greater than a right angle. ...that which has a right angle, an obtuse-angled triangle that which has an obtuse angle, and an acute-angled triangle that which has its three angles acute.
  12 KB (2,094 words) - 15:42, 1 December 2015
• 1991 USAMO Problems/Problem 1
  ...> is twice angle <math>B</math>, angle <math>C</math> is [[obtuse triangle|obtuse]], and the three side lengths <math>a, b, c</math> are integers. Determine We find that to satisfy the conditions for an obtuse triangle, <math>\beta \in (0^\circ, 30^\circ)</math> and therefore <math>\g
  5 KB (755 words) - 08:58, 6 May 2023
• 1991 USAMO Problems
  ...,A\,</math> is twice angle <math>\,B,\,</math> angle <math>\,C\,</math> is obtuse, and the three side lengths <math>\,a,b,c\,</math> are integers. Determine
  3 KB (512 words) - 19:17, 18 July 2016
• 2001 USAMO Problems/Problem 4
  ...ath> are the sides of an obtuse triangle. Assume that in this triangle the obtuse angle opposes the side congruent to <math>PA</math>. Prove that <math>\angl ...<math>PA</math>, <math>PB</math>, and <math>PC</math> are the sides of an obtuse triangle and <math>PA > \max\{PB, PC\}</math>.
  8 KB (1,470 words) - 22:24, 18 June 2022
• 2001 USAMO Problems
  ...ath> are the sides of an obtuse triangle. Assume that in this triangle the obtuse angle opposes the side congruent to <math>PA</math>. Prove that <math>\angl
  3 KB (446 words) - 09:56, 20 July 2016
• 1972 USAMO Problems/Problem 2
  ...the sake of contradiction, that each face is non-acute; that is, right or obtuse. Consider triangles <math>\triangle ABC</math> and <math>\triangle ABD</mat ...btuse and all three angles add up to 180 degrees), so the tetrahedron with obtuse triangle faces is impossible.
  8 KB (1,458 words) - 23:42, 27 February 2022
• 2001 AMC 12 Problems/Problem 17
  ...th>E=(0,4)</math>. What is the probability that <math>\angle APB</math> is obtuse? The angle <math>APB</math> is obtuse if and only if <math>P</math> lies inside the circle with diameter <math>AB
  5 KB (792 words) - 15:23, 30 November 2021
• 2009 AMC 12B Problems/Problem 13
  ...hus <math>BC = BD + BC = 5 + 9 = 14</math> or assume that the triangle is obtuse at angle <math>B</math> then <math>BC = DC - BD = 9 -5 = 4</math>. The sum
  883 bytes (137 words) - 18:42, 23 February 2017
• 2021 AIME II Problems/Problem 5
  ...eal numbers <math>s</math>, let <math>\tau(s)</math> denote the set of all obtuse triangles that have area <math>s</math> and two sides with lengths <math>4< ...6</math> and <math>14</math>, exclusive. We also have to consider the word OBTUSE triangles. That means that the two small sides squared is less than the <ma
  14 KB (2,269 words) - 00:43, 2 January 2023
• 2011 AIME I Problems
  ...andom from among the vertices of a regular <math>n</math>-gon determine an obtuse triangle is <math>\frac{93}{125}</math>. Find the sum of all possible valu
  10 KB (1,634 words) - 22:21, 28 December 2023
• 2011 AIME I Problems/Problem 10
  ...s chosen at random from among the vertices of a regular n-gon determine an obtuse triangle is <math>\frac{93}{125}</math> . Find the sum of all possible valu ...meter of the circle. (This is because if an inscribed angle on a circle is obtuse, the arc it spans must be 180 degrees or greater).
  6 KB (980 words) - 03:14, 5 May 2020
• 1999 AHSME Problems/Problem 7
  Five acute angles and one obtuse angle can only sum to less than <math>90\cdot 5 + 180 = 630</math> degrees, Four acute angles and two obtuse angles can only sum to less than <math>90\cdot 4 + 180\cdot 2 = 720</math>
  1 KB (228 words) - 21:18, 5 November 2019
• 1984 AHSME Problems
  In the [[obtuse triangle]] <math> ABC </math>, <math> AM=MB </math>, <math> MD\perp BC </ma
  13 KB (1,879 words) - 14:00, 19 February 2020
• 1984 AHSME Problems/Problem 26
  In the [[obtuse triangle]] <math> ABC </math> with <math> \angle C>90^\circ </math>, <math>
  2 KB (303 words) - 20:28, 2 October 2023
• 1985 AHSME Problems
  Exactly three of the interior angles of a convex polygon are obtuse. What is the maximum number of sides of such a polygon?
  17 KB (2,488 words) - 03:26, 20 March 2024
• 1985 AHSME Problems/Problem 14
  Exactly three of the interior angles of a convex polygon are obtuse. What is the maximum number of sides of such a polygon? Suppose that such a polygon has <math>n</math> sides. Let the three obtuse angle measures, in degrees, be <math>o_1</math>, <math>o_2</math>, and <mat
  2 KB (256 words) - 21:23, 19 March 2024
• 2012 AMC 12A Problems/Problem 22
  ...ace other than the one described in case 1, i.e. <math>t_2</math> makes an obtuse angle with <math>t_1</math>. It is possible to prove that <math>p \cap Q</m
  5 KB (940 words) - 17:13, 4 April 2020
• 1952 AHSME Problems
  <math> \textbf{(A) \ }\text{the triangle is obtuse} </math>
  23 KB (3,556 words) - 15:35, 30 December 2023
• 1954 AHSME Problems
  ...e angle and two unequal acute angles}\\ \textbf{(C)}\ \text{are always one obtuse angle and two equal acute angles}\\ \textbf{(D)}\ \text{are always acute an
  23 KB (3,535 words) - 16:29, 24 April 2020
• 1991 AHSME Problems/Problem 4
  ...le (C) An obtuse right triangle (D) A scalene right triangle (E) A scalene obtuse triangle A right triangle has an angle of 90 degrees, so any obtuse angle would make the sum of those two angles over 180. This contradicts the
  603 bytes (90 words) - 05:47, 24 February 2018
• 1991 AHSME Problems
  <math>\textbf{(C) }</math> An obtuse right triangle <math>\textbf{(E) }</math> A scalene obtuse triangle
  16 KB (2,451 words) - 04:27, 6 September 2021
• Mock AIME 6 2006-2007 Problems
  ...A,B,C)</math> in <math>R</math> exist such that <math>\angle ABC</math> is obtuse?
  7 KB (1,173 words) - 21:04, 7 December 2018
• 1962 AHSME Problems/Problem 23
  ..., we'll show that we can determine <math>DB</math> if <math>A</math> is an obtuse angle. ...ince we've determined the length of <math>DB</math> even though we have an obtuse angle, <math>DB</math> is not <math>\bf{only}</math> determined by what typ
  1 KB (256 words) - 22:39, 10 April 2023
• 1952 AHSME Problems/Problem 15
  <math> \textbf{(A) \ }\text{the triangle is obtuse} </math> ...te if <math> a^2+b^2>c^2 </math>, right if <math> a^2+b^2=c^2 </math>, and obtuse if <math> a^2+b^2<c^2 </math>. If <math> c </math> were equal to <math> 10
  1 KB (169 words) - 23:17, 2 January 2014
• 2014 AMC 10A Problems/Problem 13
  The area of the obtuse triangle is <math>\frac{1}{2}\sin{120} = \frac{\sqrt{3}}{4}</math> ...th> are right, and <math>m\angle CAB=60^{\circ}</math>. So the area of the obtuse triangle is <math>\frac{1}{2}\cdot1\cdot1\cdot\sin\left(120^{\circ}\right)=
  7 KB (1,040 words) - 02:07, 8 October 2022
• 2014 AMC 12B Problems/Problem 24
  ...sonable, since <math>10+3\approx 12</math> in the pentagon with apparently obtuse angles. Plugging this back into equations <math>(1)</math> and <math>(2)</m
  7 KB (1,037 words) - 08:09, 1 January 2023
• Obtuse Triangle
  #REDIRECT [[Obtuse triangle]]
  29 bytes (3 words) - 17:22, 2 March 2014
• 1969 AHSME Problems/Problem 28
  ...so <math>\angle APB > \angle ACB</math>, making <math>\angle APB</math> an obtuse angle. ...th> and <math>BP</math> are both less than <math>2</math>, there can be an obtuse angle that satisfies the equation, so the answer is <math>\boxed{\textbf{(E
  2 KB (280 words) - 19:57, 9 June 2018
• 1979 AHSME Problems
  If vertex angles <math>B</math> and <math>C</math> are obtuse and <math>\sin C = - \cos B =\frac{3}{5}</math>, then side <math>AD</math>
  17 KB (2,664 words) - 01:34, 19 March 2022
• 1970 Canadian MO Problems/Problem 2
  Given a triangle <math>ABC</math> with angle <math>A</math> obtuse and with altitudes of length <math>h</math> and <math>k</math> as shown in ...h>b > h</math> since it is a right triangle. Since angle <math>A</math> is obtuse we have <math>a > b</math>, or <math>(a-b) > 0</math>. Then <math>(a-b) > h
  1 KB (236 words) - 20:32, 5 June 2018
• 2006 UNCO Math Contest II Problems/Problem 1
  ...he height of the obtuse triangle is 2. We can now find the area of the two obtuse triangles and their areas are 1 and 2.
  3 KB (507 words) - 19:43, 26 November 2022
• 1988 AHSME Problems/Problem 13
  (Note that this assumes that <math>x</math> is acute. If <math>x</math> is obtuse, then <math>\sin{(x)}</math> is positive and <math>\cos{(x)}</math> is nega
  2 KB (402 words) - 20:53, 24 August 2021
• 1988 AHSME Problems/Problem 22
  ...th>x</math> is less than or equal to <math>21</math>, one of the angles is obtuse, and that the same is the same for
  1 KB (163 words) - 12:44, 10 August 2018
• 2019 AMC 12A Problems
  ...itive integer <math>n</math> for which <math>\triangle A_nB_nC_n</math> is obtuse?
  14 KB (2,180 words) - 22:25, 25 April 2024
• 2016 AIME I Problems/Problem 6
  ...adius. A simple sketch will reveal that <math>\triangle ABC</math> must be obtuse (as an acute triangle will result in <math>LI</math> being greater than <ma
  14 KB (2,397 words) - 20:04, 27 August 2023
• 2016 AIME I Problems/Problem 9
  ...This can easily be shown by drawing triangle ABC, where <math>A</math> is obtuse. Therefore, angle A is acute. Let angle <math>CAS=n</math> and angle <math>
  9 KB (1,526 words) - 02:31, 29 December 2021
• 2016 USAMO Problems/Problem 5
  ...ath> holds if <math>\angle A</math> is obtuse. If <math>\angle B</math> is obtuse then <math>\angle OAC = B – 90</math> and the <math>y</math> coordinate o
  8 KB (1,449 words) - 00:09, 12 October 2023
• 1954 AHSME Problems/Problem 19
  ...e angle and two unequal acute angles}\\ \textbf{(C)}\ \text{are always one obtuse angle and two equal acute angles}\\ \textbf{(D)}\ \text{are always acute an
  1 KB (223 words) - 01:28, 28 February 2020
• 1979 AHSME Problems/Problem 24
  If vertex angles <math>B</math> and <math>C</math> are obtuse and <math>\sin C = - \cos B =\frac{3}{5}</math>, then side <math>AD</math> ...)=-\cos(B)=\frac{3}{5}</math>. Since <math>B</math> and <math>C</math> are obtuse, we have <math>\sin(180-C)=\cos(180-B)=\frac{3}{5}</math>. It is known that
  2 KB (314 words) - 23:23, 21 June 2018
• 2017 AIME I Problems/Problem 10
  ...the diagram that both <math>\theta_1</math> and <math>\theta_2</math> are obtuse, so therefore <math>\theta_1 - \theta_2 = 0 \implies \boxed{\theta_1 = \the
  13 KB (2,252 words) - 15:46, 6 January 2024
• 2018 AMC 10B Problems/Problem 22
  ...ility that <math>x,y,</math> and <math>1</math> are the side lengths of an obtuse triangle? The Pythagorean Inequality tells us that in an obtuse triangle, <math>a^{2} + b^{2} < c^{2}</math>. The triangle inequality tells
  3 KB (509 words) - 22:17, 25 February 2024
• 2018 AMC 10B Problems
  ...ility that <math>x,y,</math> and <math>1</math> are the side lengths of an obtuse triangle?
  15 KB (2,237 words) - 23:08, 15 November 2023
• 2018 AIME II Problems/Problem 12
  ...<math>CDP</math> are obviously not congruent, we see that one triangle is obtuse and the other one is acute.(Refer to the diagram) However, if we drop perpe
  18 KB (2,912 words) - 13:12, 24 January 2024
• 2018 IMO Problems/Problem 1
  Note that triangle <math>ABC</math> may be obtuse.
  4 KB (792 words) - 01:44, 19 November 2023
• 2008 iTest Problems/Problem 56
  ...B</math>, <math>2400^2 + 2400^2 < 3840^2</math>, so <math>\theta</math> is obtuse. This means <math>\sin (\pi - \theta) = \sin \theta</math>.
  7 KB (1,092 words) - 19:05, 17 December 2021
• Mock Geometry AIME 2011 Problems/Problem 13
  Plugging in values, we find for acute and obtuse triangles denoted as <math>[1]</math> and <math>[2]</math>, respectively,
  3 KB (463 words) - 15:49, 12 July 2023
• 2008 iTest Problems/Problem 62
  ...es of <math>\theta</math> since <math>\theta</math> can either be acute or obtuse. Each <math>\theta</math> corresponds to exactly one value of <math>x,</ma
  1 KB (171 words) - 19:43, 4 August 2018
• 2000 JBMO Problems/Problem 3
  Consider the configuration where <math>\angle ACB</math> is obtuse and diameter <math>EF</math> lies on extended line <math>BC</math>.
  2 KB (367 words) - 00:35, 5 December 2018
• 2019 AMC 10C Problems
  ...r pentagon are chosen at random. What is the probability that they form an obtuse triangle?
  12 KB (1,917 words) - 12:14, 29 November 2021
• 2019 USAJMO Problems/Problem 4
  ...(*)</math> Let <math>ABC</math> be a triangle with <math>\angle ABC</math> obtuse. The <math>A</math>''-excircle'' is a circle in the exterior of <math>\tria
  10 KB (1,536 words) - 20:27, 12 April 2021
• 2019 USAJMO Problems
  ...(*)</math> Let <math>ABC</math> be a triangle with <math>\angle ABC</math> obtuse. The <math>A</math>''-excircle'' is a circle in the exterior of <math>\tria
  4 KB (652 words) - 14:21, 10 March 2024
• 2019 AMC 12A Problems/Problem 25
  ...itive integer <math>n</math> for which <math>\triangle A_nB_nC_n</math> is obtuse?
  5 KB (933 words) - 22:23, 2 January 2024
• 2019 AMC 12A Problems/Problem 19
  <math>\angle ACB</math> is obtuse since its cosine is negative, so we let the foot of the altitude from <math
  3 KB (483 words) - 16:37, 12 September 2022
• What is the definition of Pure Mathematics?
  An angle greater than 90° but less than 180° is called obtuse. An angle greater than 180° but less than 360° is called obtuse.
  35 KB (5,882 words) - 18:08, 28 June 2021
• 2021 AIME II Problems
  ...eal numbers <math>s</math>, let <math>\tau(s)</math> denote the set of all obtuse triangles that have area <math>s</math> and two sides with lengths <math>4<
  8 KB (1,429 words) - 14:31, 26 February 2024
• Pythagorean inequality
  ...^2 + b^2 = c^2</math>. This inequality extends this to [[obtuse triangle| obtuse]] and [[acute triangle]]s. The inequality states: ...s of length <math>a \leq b \leq c</math>, <math>a^2+b^2>c^2</math>. For an obtuse triangle with sides <math>a \leq b \leq c</math>, <math>a^2+b^2<c^2</math>.
  795 bytes (125 words) - 09:04, 7 June 2023
• 2021 JMC 10 Problems/Problem 13
  ...termine two angles of a triangle. What is the probability this triangle is obtuse? ...math>1^{\circ},2^{\circ}, \dots, 89^{\circ}.</math> For the triangle to be obtuse, we must have <math>180^{\circ}- A - B > 90^{\circ} \implies A + B < 90^{\c
  1 KB (160 words) - 16:16, 1 April 2021
• 2021 Fall AMC 12B Problems/Problem 8
  The product of the lengths of the two congruent sides of an obtuse isosceles triangle is equal to the product of the base and twice the triang As the triangle is obtuse, <math>a=150^\circ</math> only. We get <math>\boxed{\textbf{(D)} \ 150}.</m
  2 KB (293 words) - 22:07, 10 July 2023
• 2021 Fall AMC 12B Problems
  The product of the lengths of the two congruent sides of an obtuse isosceles triangle is equal to the product of the base and twice the triang
  14 KB (2,191 words) - 19:57, 12 November 2023
• Obtuse triangles
  ...triangle that has one angle that is greater than 90, which is called and [[Obtuse Angle]].
  100 bytes (18 words) - 14:30, 7 January 2022
• Obtuse Angle
  An Obtuse angle is a angle greater than 90.
  43 bytes (8 words) - 14:31, 7 January 2022
• Kimberling’s point X(24)
  Denote <math>T_0</math> obtuse or acute <math>\triangle ABC.</math> Let <math>T_0</math> be the base trian
  10 KB (1,751 words) - 15:34, 25 November 2022
• 2022 AMC 10A Problems/Problem 15
  ...C>25,</math> then <math>\angle B</math> and <math>\angle D</math> are both obtuse angles. This arrives at a contradiction.
  5 KB (768 words) - 21:00, 21 February 2024
• 2022 AMC 12B Problems/Problem 10
  ...an obtuse triangle, we can see that <math>a^2+b^2<c^2</math>, in any given obtuse triangle. ...}</math> is an obtuse triangle. Using the extended Pythagorean Theorem for obtuse triangles, we have: <cmath>AG^2+AF^2<GF^2 \implies 1^2+2^2<GF^2 \implies \s
  6 KB (901 words) - 22:16, 27 October 2023
• 2021 EGMO Problems
  Let <math>ABC</math> be a triangle with an obtuse angle at <math>A</math>. Let <math>E</math> and <math>F</math> be the inter
  3 KB (492 words) - 14:07, 24 December 2022
• 2023 AIME I Problems/Problem 13
  ...ped with three acute angles meeting <math>P</math>, and the one with three obtuse angles meeting <math>P'</math>. ...<math>C</math>, and <math>D</math>. Similarly, denote the point with three obtuse angles meeting at it in <math>P'</math> as <math>A'</math>, and its neighbo
  13 KB (2,130 words) - 01:52, 31 January 2024
• 2019 AMC 10C Problems/Problem 2
  ...choose 3 verticies to form a triangle and of these 10 triangles only 5 are obtuse triangles. We can do this by either counting them individually or noting th
  370 bytes (60 words) - 19:17, 9 July 2023
• Mock AIME 6 2006-2007 Problems/Problem 4
  ...A,B,C)</math> in <math>R</math> exist such that <math>\angle ABC</math> is obtuse? ...</math> (because every triangle out of these <math>13</math> points has an obtuse angle).
  878 bytes (151 words) - 02:42, 3 January 2024