An attempt to list a few of the known theorems,
as presented by the Frech great geometer, Jean-Louis Ayme,
always with synthetic proofs.
always with synthetic proofs.
All links, link to documents in his site https://jl.ayme.pagesperso-orange.fr/
under construction
[articles written in French,
unless mentioned otherwise]
unless mentioned otherwise]
- Boutin's Theorem
- Butterfly Theorem [166 pages]
- Cesaro's Theorem
- Ceva's Theorem
- Cevian Nests Theorem
- Cross Cevian Point
- Cundy's figure
- Droz-Farny Line [in English also]
- Feuerbach's Theorem [in English also]
- Fuhrmann's Circle
- Fuhrmann's Triangle's Orthocenter
- Euler's Circle
- Euler Line (H - N - G - O)
- Gauss Line
- Gray's Line (see also Ayme's Trick)
- Gray's Point (Gra - I - X_(500))
- Hagge's P-Circle
- Housel - Nagel Line (I - G - Spa - Na)
- Jacobi Theorem
- Kantor - Hervey Point
- Khoa Lu Nguyen (H - Sp - Mt - Be)
- Kosnitza Point
- Koutras' Theorem (Stathis Koutras' Theorem)
- Lamoen (van) Circle
- Lester's Circle
- Longchamps' problems
- Mannheim's Circle
- Maruyama's Rectangle
- Menelaus' Theorem
- Miquel's Circle
- Miquel's Pentagramm
- Mineur's Circle
- Morley's Circle
- Morley's Pentagramm
- Morley's Theorem [in English here]
- Nagel's Theorems (I - G - Na) , (Mt - G - Ge), (I - O - Be) (Naa-G-Ia) Be=Bevan
- Nagel Line (Mt - G - Ge) Mt=Mittenpunkt, Ge= Gergonne
- Napoleon Point
- Neuberg - Mineur Circle
- Neuberg - Mineur Line
- Newton Line of complete quadrilateral
- Pappus' Theorem
- Paracevian Perspector
- Prasolov Point (Pra - K - N) K = Lemoine Point, N= Nine Point Circle Center
- Rabinowitz Point
- Reim's Theorem
- Sawayama's Theorem [in English also ]
- Schroeter Points
- Seimiya Line
- Seimiya Line's Orthopole
- Soddy Line (Ge - I - L) L=Longchamps
- Soddy Line
- Sondat's Theorem
- Sondat's Theorem, another
- Steinbart Point
- Steiner Line
- Thébault's Theorem [in English also]
- Thee Chords Theorem
- Turner Line
- Vecten's figure [143 pages]
A few more theorems without name
- Cesaro's Theorem and a line parallel to Brocard axis
- Euler Line is perpendicular to Orthic Axis
- Kosnitza Point is isogonal to center of Nine Point Circle
- Mixtilinear Incircles I
- Mixtilinear Incircles II
- Mixtilinear Incircles III
- P - transversal of Q
Other problems (not listed anywhere else in this page)
- A circle tangent to the incircle [in English here]
- A new point on Euler line [in English also]
- An unlikely concurrence, revisited and generalized [partly in English here]
- Deux triangles en perspective ou la recherche d'un germe
- Deux segments égaux sur deux côtés d'un triangle
- Du cercle des huit points au cercle des neuf points (other 8-point circle, 9- point circles)
- First and second Ayme-Moses perspectors [in English here]
- Le triangle sommital des triangles symétrique et tangentiel (symmetric triangles)
- Le théorème de Feuerbach-Ayme
- Symétriques de (OI) par rapport aux côtés des triangles de contact et médian
- The second mid-arc point X_(178)
- Two circles, externally tangent and a third circle comes in [in English here]
- Two parallel tangent theorems [in English here]
- Géométrie synthétique "enfin libre"
- Highway to Geometry I
- Highway to Geometry II
- Highway to Geometry III
- Problèmes divers aimants et aimables 1 [contains Romantics of Geometry # 2823]
- Un point sur le cercle inscrit [a point on incircle]
- Adventitious Angles, Mahatma's Puzzle, Tantale 456 (In Memoriam of Juan Carlos Salazar)
- Apmep 162 by V. Protassov
- Crux 1671 by Toshio Seimiya
- Mathesis 1274 by Benedikt Sporkr [paracevian perspector]
- Mathscope 209, 3 [incircle in a right triangle]
Olympiad problems
- France TST 2006 p6
- IMO 1990 p1 [in English also]
- IMO 2009 p2 generalization in English
- USA Winter TST for IMO 2019 p1
Terminology - Historic Notes
Famous problems known from their figures
(In Memoriam of Juan Carlos Salazar)
[prove $BD \perp AC$]
[prove that segment $\perp$ to diameter]
Peru Geometrico
UN RÉSULTAT REMARQUABLE DE MIGUEL OCHOA SANCHEZ
... to be continued
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