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• 1995 AIME Problems
  ...the other two sides of square <math>S_{i+1},</math> are the perpendicular bisectors of two adjacent sides of square <math>S_{i+2}.</math> The total area enclo [[Image:AIME 1995 Problem 1.png]]
  6 KB (1,000 words) - 00:25, 27 March 2024
• 1995 AIME Problems/Problem 1
  ...the other two sides of square <math>S_{i+1},</math> are the perpendicular bisectors of two adjacent sides of square <math>S_{i+2}.</math> The total area enclo [[Image:AIME 1995 Problem 1.png]]
  2 KB (302 words) - 19:29, 4 July 2013
• Euler line
  Let <math>l</math> and <math>l'</math> be internal and external bisectors of the angle <math>\angle BPC, l \perp l'</math>. [[File:2 chords 4 triangles 1.png|400px|right]]
  59 KB (10,203 words) - 04:47, 30 August 2023
• Isogonal conjugate
  [[File:Parallels 1.png|330px|right]] [[File:Definitin 1.png|390px|right]]
  50 KB (8,743 words) - 18:35, 15 February 2025
• Spiral similarity
  a) <math>XO = ZO, AO = BO, O</math> is the crosspoint of bisectors <math>AB</math> and <math>XZ.</math> [[File:1938 Pras 1.png|410px|right]]
  28 KB (4,687 words) - 22:27, 19 February 2025
• 2001 USAMO Problems/Problem 4
  ...rder. Let lines <math>l_1</math> and <math>l_2</math> be the perpendicular bisectors of segments <math>AB</math> and <math>AC</math>, respectively. Then <math>l <center>[[File:2001usamo4-1.png]]</center>
  8 KB (1,470 words) - 22:24, 18 June 2022
• Symmetry
  ==Symmetry with respect angle bisectors== [[File:Bisectors 1.png|350px|right]]
  19 KB (3,291 words) - 13:44, 6 October 2024
• Feuerbach point
  [[File:Feuerbach 1.png|500px|right]] The Feuerbach point of a scalene triangle lies on one of its bisectors. Prove that the angle corresponding to the bisector is <math>60^\circ.</mat
  6 KB (1,046 words) - 14:39, 12 December 2024
• Projective geometry (simplest cases)
  [[File:Butterfly Sharygin 1.png|450px|right]] [[File:Invariant on circles 1.png|130px|right]]
  40 KB (6,966 words) - 17:36, 20 March 2025
• Sharygin Olympiads, the best
  ...with <math>\angle A = 60^\circ, AD, BE,</math> and <math>CF</math> be its bisectors, <math>P, Q</math> be the projections of <math>A</math> to <math>EF</math> [[File:2023 23 1.png|350px|right]]
  49 KB (8,447 words) - 10:27, 21 March 2025
• Symmedians, Lemoine point
  The bisectors of the external and internal angles at vertex <math>A</math> of <math>\tria ==Bisectors and antiparallel==
  29 KB (5,067 words) - 14:46, 17 March 2025