new proofs of known geometry theorems
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Here are gonna be collected (hopefully) new proofs to well known geometry theorems (mostly by Greeks), posted in the fb group Romantics of Geometry (Ρομαντικοί της Γεωμετρίας).
Each theorem will have it's own pdf, and every solution shall be in English (EN) & Greek (GR), unless mentioned otherwise.
- Butterfly Theorem, proof by Stathis Koutras, using Koutras' Theorem 5 Feb 2017 (pdf EN-GR) (origin 102)
- Desargues Theorem, proof by Kostas Vittas , using Cross Ratio 1 Dec 2016 (origin 209 in Greek )
- Droz - Farny Line Theorem, proof by Stathis Koutras 24 Apr 2019 (origin in Greek)
- Droz- Farny Line Theorem, Generalization, proof by Kostas Vittas 22 Oct 2016 (origin: mathematica.gr in Greek)
- Droz- Farny Line Theorem, Generalisation, proof by Stathis Koutras 22 Oct 2016 (origin: mathematica.gr )
- Koutras' Theorem, 22 proofs (pdf EN) (origin)
- Pascal Theorem, proof by Kostas Vittas, using Cross Ratio 21 June 2017 (origin 208 in Greek)
- Simson Line, proof by Stathis Koutras, using Koutras' Theorem 23 June 2017 (origin)
- Vittas' Theorem, proof by Grigoris Altimisis 8 June 2017 (pdf EN-GR) (origin 300)
Milton Donaire Peña
In the convex pentagon ABCDE following equalities holds: ∠ABD = ∠ACE,∠ACB =
ReplyDelete∠ACD,∠ADC = ∠ADE and ∠ADB = ∠AEC. The point S is the intersection of the
segments BD and CE. Prove that lines AS and CD are perpendicular.
we do not collect random problems here , try aops on any FB math groups
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