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• 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

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