Add new comment

Pappus' Theorem

Submitted by plusadmin on 1 January, 2001
January 2001

Let $A_1, A_2, A_3, B_1, B_2, B_3 $ be six distinct points on the plane.

$ A_1, A_2 $ and $ A_3 $ are collinear, likewise $ B_1, B_2 $ and $ B_3 $.

Let $ C_1 $ be the intersection of the lines $ A_2B_3 $ and $ B_2A_3 $.

Let $ C_2 $ be the intersection of the lines $ A_3B_1 $ and $ B_3A_1 $.

Let $ C_3 $ be the intersection of the lines $ A_1B_2 $ and $ B_1A_2 $.

Then $ C_1, C_2 $ and $ C_3 $ are collinear.

Return to puzzle page.

About text formats

Filtered HTML

  • Web page addresses and email addresses turn into links automatically.
  • Allowed HTML tags: <a href hreflang> <em> <strong> <cite> <code> <ul type> <ol start type> <li> <dl> <dt> <dd>
  • Lines and paragraphs break automatically.