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- Butterfly_theorem abstract "The butterfly theorem is a classical result in Euclidean geometry, which can be stated as follows:Let M be the midpoint of a chord PQ of a circle, through which two other chords AB and CD are drawn; AD and BC intersect chord PQ at X and Y correspondingly. Then M is the midpoint of XY.A formal proof of the theorem is as follows:Let the perpendiculars and be dropped from the point on the straight lines and respectively. Similarly, let and be dropped from the point perpendicular to the straight lines and respectively.Now, since From the preceding equations, it can be easily seen that since = Now,So, it can be concluded thator is the midpoint of An alternate proof using projective geometry can be found in problem 8 of the link below.http://www.imomath.com/index.php?options=628&lmm=0".
- Butterfly_theorem thumbnail Butterfly_theorem.svg?width=300.
- Butterfly_theorem wikiPageExternalLink TheButterflyTheorem.
- Butterfly_theorem wikiPageExternalLink ?op=getobj&from=objects&id=3613.
- Butterfly_theorem wikiPageExternalLink BetterButterfly.shtml.
- Butterfly_theorem wikiPageExternalLink Butterfly.shtml.
- Butterfly_theorem wikiPageExternalLink index.php?options=628&lmm=0.
- Butterfly_theorem wikiPageID "1335536".
- Butterfly_theorem wikiPageRevisionID "566205394".
- Butterfly_theorem hasPhotoCollection Butterfly_theorem.
- Butterfly_theorem title "Butterfly Theorem".
- Butterfly_theorem urlname "ButterflyTheorem".
- Butterfly_theorem subject Category:Articles_containing_proofs.
- Butterfly_theorem subject Category:Euclidean_plane_geometry.
- Butterfly_theorem subject Category:Theorems_in_geometry.
- Butterfly_theorem type Abstraction100002137.
- Butterfly_theorem type Communication100033020.
- Butterfly_theorem type Message106598915.
- Butterfly_theorem type Proposition106750804.
- Butterfly_theorem type Statement106722453.
- Butterfly_theorem type Theorem106752293.
- Butterfly_theorem type TheoremsInGeometry.
- Butterfly_theorem comment "The butterfly theorem is a classical result in Euclidean geometry, which can be stated as follows:Let M be the midpoint of a chord PQ of a circle, through which two other chords AB and CD are drawn; AD and BC intersect chord PQ at X and Y correspondingly. Then M is the midpoint of XY.A formal proof of the theorem is as follows:Let the perpendiculars and be dropped from the point on the straight lines and respectively.".
- Butterfly_theorem label "Butterfly theorem".
- Butterfly_theorem label "Schmetterlingssatz".
- Butterfly_theorem label "Teorema da borboleta".
- Butterfly_theorem label "Teorema de la mariposa".
- Butterfly_theorem label "Teorema della farfalla".
- Butterfly_theorem label "Théorème du papillon".
- Butterfly_theorem label "Vlinderstelling".
- Butterfly_theorem label "Теорема о бабочке".
- Butterfly_theorem label "مبرهنة الفراشة".
- Butterfly_theorem label "蝴蝶定理".
- Butterfly_theorem sameAs Schmetterlingssatz.
- Butterfly_theorem sameAs Teorema_de_la_mariposa.
- Butterfly_theorem sameAs Théorème_du_papillon.
- Butterfly_theorem sameAs Teorema_della_farfalla.
- Butterfly_theorem sameAs Vlinderstelling.
- Butterfly_theorem sameAs Teorema_da_borboleta.
- Butterfly_theorem sameAs m.04tnz2.
- Butterfly_theorem sameAs Q377047.
- Butterfly_theorem sameAs Q377047.
- Butterfly_theorem sameAs Butterfly_theorem.
- Butterfly_theorem wasDerivedFrom Butterfly_theorem?oldid=566205394.
- Butterfly_theorem depiction Butterfly_theorem.svg.
- Butterfly_theorem isPrimaryTopicOf Butterfly_theorem.
