# Dynamic Geometry 1449: Salmon Line

Given a circle O and three chords AB, AC, and AD. Circles O1, O2, and O3 are constructed with diameters AB, AC, and AD, respectively. Circles O1 and O2 meet at E, Circles O1 and O3 meet at F. Circles O2 and O3 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.

## Poster of the Salmon Line using iPad Apps

### Classroom Resource:Interactive step-by-step animation using GeoGebra

This step-by-step interactive illustration was created with GeoGebra.

• To explore (show / hide): click/tap a check box.
• To stop/play the animation: click/tap the icon in the lower left corner.
• To go to first step: click/tap the "Go to step 1" button.
• To manipulate the interactive figure: click/tap and drag the blue points or figures.

GeoGebra is free and multi-platform dynamic mathematics software for all levels of education that joins geometry, algebra, tables, graphing, statistics and calculus application, intended for teachers and students. Many parts of GeoGebra have been ported to HTML5.