Sunday, January 20, 2002

2002 #20, 21, and 22

Greatest Integer Function and Radicals in one problem? Be still my beating heart. A problem where intuition works best? Awesome. Similar triangles masquerading as a tough problem. Wow!
Difficulty: moderately difficult for students who don't see how the GIF is applied here. Of course, the resulting radicals are complicated, too.
Difficulty: Simple answer is the correct one.  Proving it is an interesting discussion.
Difficulty: Again, pretty simple if they're paying attention.

Standard instructions for this series: No calculator allowed. Express  answers in reduced form. Rationalize denominators. Radicals must be  reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest

answer 20, answer 21 and answer 22.


  1. I think you mean the triangles BDE and ABC ae similar, not congruent.

  2. Right. The triangles are similar because the angles are congruent.