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- ...math>A'B</math> to <math>AB'.</math> This fact explain existance of Miquel point. <math>C </math> is any point of <math>AB, \theta </math> is circle <math>CPx_0, C' = \theta \cap A'B'</m28 KB (4,853 words) - 22:23, 19 November 2024
- ...of <math>ABCD</math> intersect at <math>E</math>. Let <math>P</math> be a point on side <math>\overline{AB}</math> satisfying <math>\angle APD = \angle BPC Note that only one point <math>P</math> satisfies the given angle condition. With this in mind, cons4 KB (620 words) - 21:51, 18 October 2022
- ...ath>\angle PP_1C=\angle BAC</math>. Similarly, let <math>Q_1</math> be the point on line <math>QA_1</math>, such that <math>A_1</math> lies strictly between [[File:2019 IMO 2a.png|420px|right]]3 KB (479 words) - 00:49, 19 November 2023
- ...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