Merry Go Round the Triangle

Given a triangle ABC, with 3 cevians AD, BE and CF concurrent at P. Choose an arbitrary point G on AB. Draw a line GH parallel to FE to intersect AC at H. Continuing from H draw a line HI parallel to ED, etc. Click on the red buttons on the left to draw these lines in order.

 

1) What do you notice? What conjecture(s) can you make? Explore further by dragging any of the red vertices (except P).

2) Can you prove your conjecture(s) above?

Read our joint article (together with John Silvester) "A Merry-Go-Round the Triangle" published in the June 2018 issue of the Learning and Teaching Mathematics journal of AMESA.

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Michael de Villiers, created 21 March 2018; updated 3 July 2018.