A simple geometric proof of Ebisui's theorem, if two triangles
A1A2A3 and
B1B2B3 are perspective and
C3 =
A1B2∩
A2B1,
C1=
A2B3∩
A3B2,
C2=
A3B1∩
A1B3 then
A1A2 A3 and
C1C2C3 are also perspective, is given, which is using Desargues's theorem and its converse. With the theorem and an additional theorem, a (15
4, 20
3) configuration can be constructed, which is transitive both on points and lines.
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