Saturday, January 5, 2002

2002 #5 and 37

Geometry rules. Then number theory.
Difficulty: Not too bad. Arc length, anyone?
Difficulty: Just algebra. Okay, there's some heavy lifting here, but LOTS of stuff cancels.

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 05 and answer 37.


  1. Okay, I've got the second problem down to


    Now, I'm stuck. Where do I go from here? (or am I completely off track)

    Also, according to my calculator's equation solver, I get 1/2 as the answer, not 7/2.