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  • '''Isogonal conjugates''' are pairs of [[point]]s in the [[plane]] with respect to a certain [[triangle]]. ...r of lines symmetric with respect to <math>\ell</math> and containing the point <math>O</math> be called isogonals with respect to the pair <math>(\ell,O).
    54 KB (9,416 words) - 07:40, 18 April 2024
  • ...iangle <math> \Delta{A_1}{A_2}{A_3} </math>. These masses then determine a point <math> P </math>, which is the geometric centroid of the three masses and i For any point in the plane <math>ABC</math> there are <i><b>barycentric coordinates(BC):
    34 KB (6,879 words) - 16:36, 2 February 2025
  • Let point <math>E</math> be symmetric <math>D</math> with respect <math>\ell.</math> [[File:Bisectors 2.png|350px|right]]
    19 KB (3,291 words) - 12:44, 6 October 2024
  • Let <math>b\geq2</math> and <math>w\geq2</math> be fixed integers, and <math>n=b+w</math>. Given are <math>2b</math> identical black [[File:Peppa-usamo-2022-2.png|800px]]
    7 KB (1,337 words) - 01:08, 9 January 2024
  • Let <math>ABC</math> be a triangle with orthocenter <math>H. P</math> is a point on the circumcircle <math>\Omega</math> of <math>\triangle ABC.</math> ...th>H</math> are collinear. Respective line is known as the Steiner line of point <math>P</math> with respect to <math>\triangle ABC.</math>
    14 KB (2,381 words) - 11:07, 12 May 2024
  • ...<math>AB</math> has the ends on the sides of a right angle and contains a point <math>C(x_C, y_C).</math> Find the shortest length of such a segment. The rod is fixed at point <math>C</math> on a hinge without friction. The hinge allows the rod to rot
    12 KB (2,104 words) - 13:11, 24 February 2024
  • so the system of the equations define the only tangent point of the circle and the line. ...er, <math>O'</math> is the incenter <math>\triangle KK'L, F'</math> is the point of tangency incircle of <math>\triangle KK'L</math> and <math>KK'.</math>
    48 KB (8,214 words) - 07:59, 30 July 2024
  • ...pace. To each point <math>A</math> of plane <math>\Pi</math> we assign the point <math>A'</math> of plane <math>\Pi'</math> at which the line <math>AO</math ...ng which it intersects the plane <math>\Pi</math> as <math>\ell.</math> No point of the line <math>\ell</math> has an image in the plane <math>\Pi'.</math>
    39 KB (6,959 words) - 14:26, 3 December 2024
  • ...ath>\angle PAB = \angle PBC = \angle PCA.</math> Prove that there exists a point <math>Q</math> on another median such that <math>\angle QBA = \angle QCB = ...ect to a circle <math>\Omega</math> is <math>CD^2</math> so the power of a point <math>D</math> with respect to a circle <math>\omega</math> is <math>CD^2.<
    46 KB (7,965 words) - 14:29, 17 November 2024