Ken's Puzzle of the Week

Overlapping Triangles

  1. Draw three triangles, such that each overlaps a different vertex of the other two.  That is, in triangles A,B,C with vertices (A1,A2,A3), (B1,B2,B3), (C1,C2,C3), you'll find B1 and C2 inside triangle A, C1 and A2 inside triangle B, and A1 and B2 inside triangle C.
  2. Repeat #1 with identical right triangles.  Can you do it with isosceles right triangles?  What is the smallest internal angle possible in the triangles?
  3. Repeat #1, placing all vertices on grid points.  What is the smallest rectangle which holds all three triangles? 

Source: Original.

Update 1 June, 2010. I'm no longer maintaining this site regularly. I'll keep the title, since that's how it was originally named. I hope to still provide occasional puzzles.  Solutions are welcome, but it may be a long time before I update them.
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