Given a circle O and three chords AB, AC, and AD. Circles O_{1}, O_{2}, and O_{3} are constructed with diameters AB, AC, and AD, respectively. Circles
O_{1} and O_{2} meet at E,
Circles O_{1} and O_{3} meet at F. Circles O_{2} and O_{3} meet at G. Prove that (1)
C,G,D are collinear; (2) C,B,E are collinear; (3) B,F,D are collinear) (4)
E,F,G are
collinear, the line EFG is called the Salmon line.

George Salmon (1819
- 1904) was an Irish mathematician and professor of mathematics at Trinity College Dublin.

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Ten problems: 1411-1420

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Circle

Diameters and Chords

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Collinear Points

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Simson line

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